They said they had plenty of remote-friendly teams and started setting up manager interviews. Then one by one, they called back to say that team was either no longer hiring remotely or outright frozen. Even the ones that said they had team members all over the world. A few times they asked me to consider relocating, I declined. Eventually I did get a revised offer for a remote team, but it was less than my current comp. They revised upwards each time I declined or outright said goodbye. The last (and best) offer I got before they stopped calling was roughly my existing comp and level at the time, while being remote like my existing job. It wasn't worth switching for the same thing.
So clearly wanting remote was a negative bargaining chip even though my current job is/was remote. Long story short, I also determined that they really only wanted me if I disliked my current job enough to leave without an upgrade, as others had done in my shoes. Nothing personal in the end, just observing their moves.