BA's policy is quite reasonable imo

If you only purchase a ticket with BA to BKK, it is not going to take responsibility/liability for it for the onwards flight. Book a through ticket and the benefits of a through ticket are provided

In the other example, it read to me that 4 people were travelling from GVA-LHR and then 1 person was travelling on to HKG.

The allowance is 1 per person and does not cumulate as a family group, so only 1 bag would be entitled per person to be checked through

BA are not being difficilt, just simply proving that which has been paid for. If a passenger wishes to buy separate tickets, then the passenger needs to accept that there are also drawbacks of separate tickets