I'm really sorry, but I'm afraid I think your teacher was right in marking that answer as wrong.
Disclaimer: I am not an ESL (English as a Second Language) teacher, so you could argue I don't really know what's standard on ESL exams. You should try to get a second opinion on the ELL StackExchange, where you are quite likely to have your question answered by an ESL teacher.
Having said that, let me explain why I think your teacher is right.
On the one hand, I agree with you that
Tom told me that he might/could be very rich when he's 35.
has the same meaning regardless of whether might or could is used. Oh, some people may claim to detect some subtle difference between the two, and probably one can invent contexts where this difference may even be real. But in the most likely meaning of the sentences, I don't think there is any difference most native speakers would agree on.
On the other hand, in the context of an exam, when a teacher asks for reported speech, what is really being asked for is a minimally modified version of the original text such that the new version nevertheless counts as reported speech.
Note that, in general, conversion to reported speech is not unambiguous. For example, if a speaker says I, in the reported speech this may be transformed into she, Julia, the woman on my left, etc. This is why teachers must be careful when composing exam questions, and flexible as far as what answers they allow.
But it is very standard to insist that no unnecessary changes should be made; otherwise the question would be about paraphrasing as opposed to reported speech.
And, unfortunately, the change from could to might is not a necessary one. True, the meaning is unchanged, but that's not the point. All kinds of paraphrases would leave the meaning unchanged. That's not what the question was about. So, I'm really sorry, but I think your teacher is right in marking that question wrong.