BGP is not solved if there is Sybil attack vulnerability.
In bitcoin, BGP is solved to within the stated tolerance of 51% byzantine faulty nodes.
Satoshi's PoW does not distinguish between faulty and non-faulty nodes.
The following is not "other attack" but rather it is a Byzantine fault (because the loyal participants can't be certain of Consistency by keeping the control of the hashrate below 51%).
There is no way to distinguish a 51% attack from a non-attack, e.g. for example censoring transactions, in a way that is provable with block chain data (i.e. to an offline node that comes online). One of the key innovations in my design, is it is possible for a payer to send his PoW share away from a "pool" (not example the same as pool in Bitcoin) that is provably (from that payer's individual perspective) responsible for censoring the transaction.
Since nothing about faults is provable from the block chain, then there is no provable Consistency (w.r.t. to what loyal nodes would consider a fault, e.g. censoring txns) and thus the BGP has not been solved.
We use community monitoring to estimate that we have Consistency, but this can't be proven objectively just from the block chain. We must correlate user experiences and other data points such as pool concentration.
A Sybil attack against the means by which loyal participants determine whether 51% control has been perhaps ceded to pools removes one of the key data points.
So we can conclude Bitcoin didn't solve BGP because there is no block chain objectivity about faults. And then we can say that Sybil attacks on pools destroy one of our subjective metrics for community appraisal of Consistency.