FB are large enough that they do a ton of their own very low level work - up to and including things like their own bespoke datacenter switches and SDN platform, stuff which is almost wholly distinct from what their core product is. (https://engineering.fb.com/2019/03/14/data-center-engineerin...)
It seems entirely possible that, even putting aside the PR, they're concerned about making sure a robust modern systems language stays around/thvives so that they have a robust modern systems language to use.
There are a lot of teams within Facebook that use Rust, and a lot of things that could be improved with Rust that would benefit Facebook as well as everyone else.
Someone correct me if I'm wrong, but based on the Rust Foundation website, it looks like the point of the organization is mainly to allocate funds to pay people to do work relating to the Rust language and community. So it seems like paying for a board seat means you get to indirectly influence the direction of Rust by deciding which parts people get paid to work on, and which parts are stuck with unpaid volunteers. I don't necessarily see anything wrong with that, it's good to see people get paid and the people paying should have a say in it, but it seems different from people claiming that paying for a board seat doesn't give them any additional influence over Rust.