Nobody ever said BA NEVER comp's, as Gaza said, they just don't do it based on showing them a UA 1P card or something like that.
In the ECCCA program there were often a set amount of cards based on company revenue. Also, certain regions would have their sales managers hand out a card to high revenue passengers. As always, anyone who could prove high revenue in advance could always request a card, and I'm not talking about the UA 1K's that make top-tier for $6000 as that is usually the price of just one ticket on BA...
On FT A "comp" is usually referring to a status match, that is something BA doesn't do. When it's a comp as in complimentary then yes, BA does have procedures in place for that.