I don't have my grammar book with me now, but I have strong feel that sentences like "Io ho scarpe" or "Lui beve acqua" are grammatical incorrect in Italian.
Yes, you can find them in some situations like dialogues between friends or in poetry, but the object of the verb must have something in front of it to be grammatical correct.
It might have a definite article: "Io ho le scarpe". Or
It might have an indefinite article: "Io ho una scarpa". Or
It might have a partitive article as: "io ho delle scarpe" (an unspecified quantity of shoes). Or
it might have indefinite adjectives as: "Io ho alcune scarpe".
I get the feeling that this is incorrect, and that we havn't learned the correct way yet. Romance languages are filled with articles and it seems like there needs to be some form of "de" in there. I've no idea what it is in Italian, but in French for example, "J'ai DES chausseures"
This showed up as one of the examples for "I have shoes" in http://mobile.reverso.net/en.
Ho scarpe, buoni cappelli e oltre 100 cravatte. [ I have shoes, good hats and over 100 ties. ]
And another example:
Questa giacca non ho tasche per gli occhiali. [ This jacket has no pockets for glasses. ]
Perhaps what would be useful is that Duolingo indicates that a particular phrase is a slang or conversational, and it is not accepted for a written test.