I'm pretty sure it would be legal, as long as everyone was properly identified and recorded.
the blind leading the blind here, but that claim is probably false.
The buyer would send the seller BTC, and the seller would buy the stocks in HIS brokerage account.
though the jurisdiction wasn't mentioned, nearly everywhere it is illegal to manage the funds of others for trading unless registered to do so (e.g., as a brokerage or as a qualified custodian)
The seller then transfers the stocks to the buyers brokerage.
in the u.s., the "travel" rule would give the full trail (including account info) of the transfer from one exchange to the next.