Correct me if I'm wrong, but my understanding is that cryptographic and non-cryptographic hash functions have similar avalanche properties (and therefore similar probability of accidental collision); the difference is just that cryptographic hash functions make it difficult to intentionally create a collision.

Is that right?

Good non-cryptographic hash functions have "good" avalanching behaviour, but the definition of "good" depends on how randomly you expect your inputs to behave and how much a collision costs you. In hash tables, for instance, people often use quite weak -- i.e., poorly avalanching -- hashes since the cost of a collision is quite low.

Probably the best way to phrase it is that non-cryptographic hash functions cover a continuum with checksums at one extreme and cryptographic hash functions at the opposite extreme.