In my understanding, "sen nenia tim'" would mean the same as "kun ĉia tim'"

Well the way to test what interpretation would in practice be put on sen nenia timo is to ask in the Esperanto forums.

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For me, "sen nenia timo", "sen ĉia timo", "sen ia timo" and "sen ajna timo" would mean the same as "kun nenia timo", but "kun ia timo" and "kun ĉia timo" would mean the different things.
In Russan, "без никакого страха" (sen nenia) would sound strange, but "без всякого страха" (sen ĉia) and "без какого либо страха" (sen ia) would be normal expressions.

Always when it comes to negated sentences, or questions, or words like "some" and "any", one have to be very careful in international communication. Esperanto has not solved those problems once for all. (What it has done is only that it has collected most of them as tabelwords.)
One example of negative ambiguity. Bertilo writes in "Detala gramatiko" about the two systems of responding negated phrases:

Ambaŭ sistemoj respondi al neaj demandoj, estas logikaj, sed en malsamaj manieroj. Estus bone, se nur unu sistemo ekzistus en Esperanto. Principe oni povas rekomendi la okcidentan sistemon, ĉar ĝi estas ĝis nun la pli ofte uzata, kaj klare la pli ofta ĉe Zamenhof. Sed ŝajnas, ke ne estas eble atingi tute unuecan uzon de unu sola sistemo. Ambaŭ uzoj estas hejmaj en la lingvo. Oni tial estu singarda pri respondado al negativaj demandoj. Oni prefere aldonu klaran respondfrazon por ne riski miskomprenon.

Both systems answer negative questions and are logical (Sic!), but in different ways. It would be opportune if only one system existed in Esperanto. In principle, the Western system may be recommended, because it is currently the most frequently used, and also clearly most commonly used by Zamenhof. But it seems that it may not be possible to reach a completely unified use of only one system. Both usages are at home in the language. It is worth being careful in answering negative questions. It is helpful to use a clear sentence as an answer, so not to risk misunderstanding.

Another example. A Swedish newspaper once long ago wrote something like: "Vi har upprepade gånger varnat Napoleon för att lägga sig i andra länders angelägenheter."
A literal translation would be "We have repetedly warned Napoleon for interfering in other countries' affairs." I think in English one would say "...warned Napoleon not to interfere.." which for Swedish ears sounds illogical. The two words "warn" and "varna" are so similar, but one of them contains a negation which the other one does not have.

sudanglo:Have you come across any good examples in the 4 million words of the Tekstaro, where you have to know the mother tongue of the author to understand what he is getting at?

I tried to find out if "averti" + infinitiv could be such a case, where some writer use the "English" system, where you state the desired action after the verb, while other use the "Swedish" system, where the thing that should be avoided is stated. I only found one "averti" + infinitive. It was according to the Swedish system. It was found in "Pro Isxtar". In all other cases "averti" was used in quite other constructions (with full phrases, the preposition "kontraŭ" etc) making the meaning clear.
I will continue being alert when I meet "avertVF" + infinitivo.

I was translating a poem written in Afrikaans by Mathiews Phosa. The original text is given to the left, the Esperanto translation to the right:

so is die lewe tia estas la vivo
hy hou jou aan 'n lyintjie li tenas vin sur lineto
al wat troos la nura ( "ĉio" ), kio konsolas
is dat goeie dade estas, ke bonaj agoj
nie saam met jou sterf nie ne mortas kune kun vi

I wanted it to be a quite literal translation, because it was to be part of an Afrikaans teaching material. The first lines were easy:

so is the life
he holds you at a thin line

But after that comes the problem:
everything that consolates
is that good deeds
do not die with you

The problem is al = all, everything.

For me as a Swedish speaker - especially with my specific dialect background - the construction is understanable, and conforms with Swedish expressions. But I would not transalate it as "everything" or "all" - and not as "alles" if I were to translate it into German. And I did not translate it as "cxio". Because it doesn't seem quite logical to me. I don't feel confident that it would be properly understood. I chose "la nura".

How does it come that "cxio" can become "la nura"? They seem to be opposites. Cxiu is much, la nura is little.
There is a logic behind. There are just some subcomprehended steps, and which these steps are, is certainly not obvious to all.

I think the first step was that it became a fixed phrase to say "all that remains" instead of "the only thing that remained". The word "remain" makes it obvious that you don't look at the real stuff, but a sort of negation of it, the leftovers when you remove it. "All...is" shows that even if you make an effort to collect all of the remainder, still it is not more than.... It is not more than two lines in the poem. In the poem the word "nur" was not necessary to indicate that these two lines was not much, because the reader could see that they were just what was written on these two lines. And the word "remain" was not necessary, because the reader would by the formal analogy see that the phrase indicated that a remainder was discussed.
I don't know in how many languages a literal translation of this line of the poem would work.
In Esperanto the comprehension becomes even harder than in English, because commas are used before all subphrases, whether they are extending or restricting the meaning of the main phrase.

@Rugxdoma: Just to add another language to your very interesting post: El único consuelo es que los buenos hechos no (se) mueren (or morirán) contigo (or con usted or con vos).

About "all that remains" and "the only thing that remains":
In Spanish "todo lo que me quedaba" and "lo único que me quedaba" can be used interchangeably in most cases.

Bemused:Note:
1) What is written above is consistent with the rules of English spelling, which demonstrates how often those "rules" have exceptions
...

Well, actually, no the examples you gave of supposedly phonetic spelling do not conform to my dialect of English. As I mentioned before, that is why alleged English spelling reform is so bedeviled. Whose English?

And, again, that is why the pronunciation and orthography of Esperanto are so estimable, even if some speakers "pull" the pronunciation somewhat.

Hispanismo or not, Google Translate renders sen nenia timo as 'without any fear' and translates it into each of the European languages I tried with a similar meaning.

Kukolo finds a number of hits on the net. Would they all come from Spanish speakers?

Incidentally, the use of 'ajna' seems relatively recent in Esperanto to judge by the hits in the Tekstaro.

sudanglo:Hispanismo or not, Google Translate renders sen nenia timo as 'without any fear' and translates it into each of the European languages I tried with a similar meaning.

You can not be serious considering Google Translate as a valid reference …
The fact remains that in Esperanto a double negative turns into positive. That's not open for interpretation.

Fenris_kcf:
The fact remains that in Esperanto a double negative turns into positive. That's not open for interpretation.

You should never use no double negatives, anyway.