Is it only humans who can understand Buddhism? If Buddhism is a general theory of understanding the cycle of attachments, is it possible that any other 'wise' enough creature could achieve the same thing? 

In the Visuddhimagga English translation,  a creature who can understand this theory is called 'a wise man'.

In the Visuddhimagga Sinhalese version,  a creature who can understand this theory is called as a creature with 'Trihethuka Pratisandi'. i.e. Tri (three) + hethuka (caused by factors) + Pratisandi (birth): 'A birth caused by three factors' (Pali: tihetukapa.tisandhi).
Actually, the restriction has nothing to do with being a human; it has, as the Visuddhimagga notes, everything to do with the rebirth-linking consciousness (patisandhi). Nor does it relate to "understanding Buddhism" per se, but rather attainment of samatha jhana and nibbana. Only a being who is reborn with all three of the wholesome roots - non-delusion (amoha), non-greed (alobha), and non-anger (adosa) can attain absorption (jhana), the path (magga) or fruition (phala).

Types of beings that may be born with these three roots are humans, angels (deva) and gods (brahma). Animals, ghosts and hell beings are not.

For more information, here's a good summary of the types of rebirth based on number of roots:

http://www.wisdomlib.org/buddhism/book/abhidhamma-in-daily-life_2/d/doc3181.html