Also in such a question, not using "czy" could feel as if you're making sure your interlocutor remembered to take something which he was supposed to take: imagine asking a friend "Masz pieniądze?" (she was supposed to bring money she owed you) or "Masz zioło?" (Do you have the weed? - he was supposed to bring the weed).
It's obviously not that it has to be like that, but not using "czy" at least opens the gate to such an interpretation, while "Czy masz" should be a simple question about whether you have something or not.
Because in that sentence they did not, that's exactly why.
"mieć" (to have) takes Accusative, which for masculine inanimate nouns (like "basen") is identical to the basic, Nominative form.
Whenever you negate a verb that used to take Accusative, it takes Genitive instead - which is "basenu". That's what you had in the other sentence.
Other cases don't change when negated.