Fingerprints and amniotic sacs

I was recently reading about telling twins apart, which linked to this article, which includes the paragraph:

Searching around, this idea seems to be somewhat popular, but there doesn’t seem to be a mechanism mentioned, and I don’t find it believable. How would this theory be of fingerprint occurrence have been invented, tested, and validated? What’s the process here that I’m unaware of?

My reading of the scientific literature doesn’t mention that theory at all. The consensus seems to be that the processes governing fingerprint formation are unknown but genetics makes some contribution.

The timing is also wrong. From here and here, fingerprints form between 10 and 19 weeks. At six weeks, the fingers haven’t even separated.