Earlier quoted context omitted.
That being said md5 does generate collisions. I was playing with the IMDB movie database that you can download. They use a combination of the title and the year as a primary key. I tried using an md5 instead to save space (but giving a reproducible ID instead if an identity column), and got many collisions. No collision with SHA256.
Oh, of course md5 has collisions. It's relatively easy (not computationally easy, but there are known methods) to find two random strings that hash to the same value, it's just very difficult to find a string that hashes to the value of a specific other string.
Yes, collisions are easier than preimages, but they still shouldn't occur by chance in real applications!