If he has a butt.
The Doctor sweats and cries, can simulate a fever... But can he fart?
He can produce the sound, but not from squeezing gas through a tightened sphincter unevenly, just probably the same place his speaking voice comes from... Even if they had really wanted to, holographic gas can squeeze through a holographic sphincter creating a "real" farting noice, because the Doctor is moving parts inside moving parts like any other piece of fine clockwork, so it wouldn't be impossible.
Its the 24th century!
They must have taken some real steps towards smellovision by the 24th century!
What's the point of faking a fart or a burp if it doesn't smell like a fart or a burp?