Repeating that this process doesn't appear to be using cryptographic hash functions in the first place, so this conversation isn't relevant, but:
Only in the sense that "we don't know of a way to generate a new sample that has the same hash, yet". Unless we can prove P!=NP, we can't even prove that there exist hash functions that are actually infeasible to generate a sample with the same hash - so far we are no where close to knowing whether P!=NP or P=NP.
Even if we assume P!=NP, that doesn't mean that it is infeasible to generate collisions for our current cryptographic hash functions. They're not backed by some mathematical proof of correctness assuming , just the fact that so far no one has publicly figured out a way to break them, and the people who spend time trying think that their design is one that is unlikely to be broken in the near future.
We have managed to find collisions against hash functions that we previously considered cryptographically secure, that were designed with the same sort of standard in mind: E.g. md5 (https://en.wikipedia.org/wiki/MD5#Collision_vulnerabilities) and sha1 (https://en.wikipedia.org/wiki/SHA-1#Birthday-Near-Collision_...).
There's no great reason to think that private groups could not have an attack against current hash functions [1], and there's definitely no reason to think that they won't find one in the future.
[1] There sort of is for SHA2, and that's that bitcoin has effectively created a giant bounty for breaking it.