That's incorrect.
BXT was/is mainly distributed as a reward for providing liquidity in selected LPs on Hive Engine.
BXT swapping rewards (that changed to SWAP.HIVE a few days later) happened long after Beeswap got the market share. Ironically, they were introduced when Beeswap started losing the market share to uswap/kswap that understood the SWAP.HIVE "unpegging" issue first. If you look at BXT staking rewards going south (currently under 8% APR on an inflationary token), you can understand the business has issues.