No, the seller pays the 6% commission to their agent and then their agent gives the buyer's agent half of it. That's how it works everywhere in the US.
This is all important because there's a layer of legalities and agency relationships that the public completely ignores, but is relevant if we're going to have a conversation about commissions. It's also relevant because some states have begun to change their laws to be more in line with what the public thinks happens, which has its own weird twists.
*Brokers and lawyers in the audience will probably say I'm still handwaving away some nuances here regarding agency laws. Mea culpa, I'm trying to keep this simple.