[Tarto]

No, I think I misunderstood. I made a confusion between "as opposed to some other language" and "but not other languages", which indeed have different meanings.

I am not a native Japanese speaker, and you may have guessed that English is not my first language either. However I intensively studied the language in Japan and now I use it everyday at work (I'm the only foreigner in my company and nobody speaks English). Also, I mostly hang out with Japanese people and I am still studying Japanese with a private teacher.

While I don't have the pretention to speak a perfect Japanese (I consider myself to be still very far from that goal), I am confident regarding the は and the contrast thing.

Maybe there was some confusion in what I wrote. What I don't agree with is the fact that は+potential "definitely carries" the expression of a contrast, I would replace that with "can carry". It is true that between が, は and を, only は can express a contrast, but it also has other usages.

For the sake of clarity, let me give some examples of how the same expression 日本語は話せます can have different meanings depending on the context. Note that intonation is very important to convey the proper meaning:
1) as an explicit contrast: you gave a perfect example

2) as an implicit contrast: let's say someone has implicitly stated that you couldn't speak Italian. In that case, if you say for instance でも日本語は話せます, it means "but I can speak Japanese" (as opposed to Italian). My guess is that the textbook you mentioned was referring to that kind of situation. In that context, it is important that you put the stress on the word 日本語.

3) as an emphasizer: when someone asks you if you can speak Japanese, or doubts that you can speak Japanese, you can reply 日本語は話せますよ, putting the stress on 話せますよ. It means "I can speak Japanese", slightly implying "of course I can", therefore making it unsuitable when you must be very polite because it is a little too direct. This is perfectly ok in most everyday situations though.

4) Other than that, it's the "regular" は that just means you can speak Japanese.

PS: you are totally right regarding the できる thing, the same goes with many other words/expressions, for example the commonly used よろしくお願いします, where it is more natural to write よろしく than its kanji equivalent 宜しく.