What's been done here is a chosen-prefix collision attack [1] where the attacker can produce two files that have the same hash. What you're asking about is a preimage attack [2] where one of the files is already created and the attacker can't influence it.

The practical attack enabled here is mostly around digital signatures. An attacker could produce documents A and B that both have the same SHA-1. They can then get someone to sign document A (which really is signing the SHA-1 of document A), then use the signature with document B and make it look like they have a document B signed with a valid signature.

As an example, if document A is a regular SSL certificate request, and document B is a "CA certificate", the attacker can trick a real CA into signing a rogue CA into existence, which can then sign its own certificates that will be trusted by every browser. This has already happened with MD5 in 2008 [3].

[1] https://en.wikipedia.org/wiki/Collision_attack

[2] https://en.wikipedia.org/wiki/Preimage_attack

[3] http://www.phreedom.org/research/rogue-ca/

It should be noted that certain modern signature schemes (such as ed25519) are fine with just preimage resistance.

Even MD5 is still strong against that sort of attack

This is not a preimage attack.