"exclusions apply" - generally said to be capacity based for the BA lounge.
When you are flying business on Qatar from SFO, I understand they prefer you to use the Air France lounge with whom they have a contract.
Those flying other OW airlines are not able to use that lounge.

I don't think it would particularly have mattered if you had status with BA, despite what the agent said.
There are often reports on here of being denied entry to BA lounges in the US when flying another OW airline (usually AA).
I have been (politely, usually) denied access to both IAD and PHL BA lounges in similar situations in the past.