Minor nit: note that a collision after the first MD5 application will result in an HMAC-MD5 collision. The dissimilarity between the two MD5 applications isn't for collision resistance. (The second MD5 application is still mandatory for preventing length extension attacks, and makes key recovery attacks more difficult, among other things.)
Rather, the increased collision resistance comes from the fact that the 64-byte keyed padding puts the MD5 context in a state unknown to the attacker before any of the attacker's data touches the MD5 state. As long as the HMAC key has at least 128 bits of entropy, all possible values of the 128-bit MD5 internal state are nearly equally likely. This makes it much more difficult for an attacker to produce collisions.
Rather, the increased collision resistance comes from the fact that the 64-byte keyed padding puts the MD5 context in a state unknown to the attacker before any of the attacker's data touches the MD5 state. As long as the HMAC key has at least 128 bits of entropy, all possible values of the 128-bit MD5 internal state are nearly equally likely. This makes it much more difficult for an attacker to produce collisions.