The way a Czech speaker explained it to me is that the first word is the stressed word, which in this case is No. The speaker is making a correction. The last word is the secondary stress, in this case já (I), similar to how it would be emphasized in English. So I think you are both right. Another way to think about it is as two clauses, each with their own emphasis.
Well, yes. It also depends on the sentence. In the basoc SVO order you can emmphasize any word.
JÁ jsem Matěj.
Já JSEM Matěj.
Já jsem MAŤEJ.
Other word orders will only be possible when you strongly stress the last unit.
Matěj jsem JÁ.
I intentionally avoided the word stress for it is a complicated linguistic concept and it may not be the thing I have in mind. I just used the word "to stress something" in the everyday meaning, not the linguistic "sentence stress".
I would just point out that "random order" suggests that any word could be placed anywhere in the sentence. While there is much more flexibility in word order in languages like Czech and Russian, sentence structure is not random -- though it may seem to be to those who are learning a language that often doesn't follow the patterns of English!
The correct English phrasing closest to what BaloghTams19 is asking after is "Matěj is who I am." However, I suspect that this would be worded differently in Czech. (I know that it would be worded differently in German, although of course German is far more closely related to English than is Czech.)