Well, yes, that too, but the mapping is most definitely not one-to-one.
The primary translation "Matěj has not got meat" sounds rather stiff. I didn't check whether "Matěj doesn't have meat" is accepted (I assume it would and I think it should), but I think on, at least, a colloquial level of style "Matěj has no meat" would be considered equivalent to "Matěj has not got meat", since the former implies the latter, at least without any context to judge whether he doesn't have the specific meat or no meat at all; without context also "žádné" is a bit superfluous.
I stand by my opinion, that "Matěj has no meat" should be accepted.
I'm reacting to your multiple negations question: Both.
Simple "ne-" acts similarly to English
"to není neobvyklé" = "it is not unusual"
Fun begins when we want to translate sentences with words like "any", "each", "none", "never", "no one" or "nowhere"
"nic nevím" = "I do not know anything"
The wildest possible example could be "Nikdy jsem nikde nikoho neviděl". Literally it would be "I have not never seen no one nowhere", but it has to be understood "I have never seen anyone. Anywhere."
In english can be in one sentence only one negation (that is what i was taught in the school) In czech you can put multiple negations in one sentence.
They do not cancel each other out. And i don't think that they strengthen each other. It's just the way how to express negative statement in slavic languages.
For example: Nikdy to nikomu neříkej.= Never say it to anybody (which literally translated to czech is Nikdy to někomu říkej.)
I am not convinced by your point. Czech and English are languages that work in a different way and to what the negation links, does in this case not make any difference semantically. I'd even go as far as arguing that "Matěj nemá žádné maso" in fact is a quite far reaching translation of "Matěj does not have meat", rather translating it as "Matěj does not have any meat".
Maybe to rephrase it in yet another language, for emphasis. I think that "Matěj maso nemá" maps to German "Matěj hat kein Fleisch", to which "Matěj has no meat" maps as well, whereas "Matěj nemá žádné maso" would map to German "Matěj hat gar kein Fleisch", which is semantically different.
I agree that English 'I do not have meat' and I' have no meat' mean the same thing. On the other hand, each of those has a different literal translation into Czech.
The particular Czech sentence in this exercise happens to use the form that means 'does not have' rather than 'has no'. So I think the DL team is within their rights to insist on that English phrase, especially since there is a different Czech phrase available if the other is meant.
In deciding how to translate a sentence -- and especially when teaching a language to foreigners -- semantic equivalence is not the only criterion to apply. For example, when I introduce myself, I might say any of the following:
1. I am Bill. 2. My name is Bill. 3. I am called Bill.
But are these three really all the "same"?
I would never never never say "Matej has not got meat." If I wanted to talk about Matej not having meat, I would say "Matej has no meat" or "Matej doesn't have meat." And those people who are saying that "Matej has no meat" is not the same in practical speech as "Matej doesn't have meat" are not correct in my experience. There is no difference in meaning or emphasis or emotional content between the two.