Well if someone can come up with valid signatures for one fork and someone else merely has a fork claiming to be valid but can't produce signatures, it is pretty clear which one will be more credible.
Yeah except the longer fork could claim the signatures are missing. And they could be for UTXO that have not yet been spent on the other fork, so there is no way to show that one fork has signatures for those UTXO and the other doesn't. And you could have a bunch of valid signatures for recent time window wherein signatures are not supposed to be yet discarded. So then how do you prove those old UTXO were not signed for? You need for the owners of those UTXO to sign a message saying they didn't yet spend their outputs. If the adversary had some way to determine which UTXO are those where the private key has been lost, he could steal them this way.
Sounds far-fetched though.
I don't necessarily see a big problem here. That was crypto_zoidberg's argument, and for that reason he put the chain (with signatures) on a web site. Though I don't think it has been updated.
In Bitcoin it is already the case with UXTO pruning that if no one voluntarily saves the whole chain the system is pretty screwed.
I don't see "major vulnerabilities" here.
Re-reading the context where "nullc" commented (didn't realize before that username is Maxwell), I think he means in that in the context that BBR would be fully supporting a SW (segregated witnesss) with proof-of-fraud as the security model. Apparently Maxwell took peanutbuttercoin at his implication that BBR had implemented the SW security model, which in fact BBR has not really. So Maxwell's comment is due to a failure of communication as to what BBR has actually implemented. SW security model requires proof-of-fraud, which requires being able to prove which signature was used for a transaction so it can be shown the signature was invalid in the proof.
Edit: someone might want to make a clarifying post on the Reddit subthread. I am not going to do it.