You can't get a BFTA card unless you are a member of a club that is insured and can present a copy of that insurance cover.
If the cover on the day of the event effectively falls to the policy held by the host club, then presumably the restriction on who can have a BFTA card is irrelevant. Their own club's insurance policy is not involved on the day, and in any case the club insurance doesn't extend to personal cover.
The BFTA requirement that all club members had to have a BFTA card if the BFTA insurance was to be valid ignored the fact that many clubs are multi-disciplined, and do a lot more things than just FT. Somebody who is a 10m pistol shooter doesn't need a BFTA card. Likewise if the club is affiliated to IPSA is it reasonable for them to require all FT shooters to be registered card-carrying pistol shooters?