I only chose teams to put on the website that really use it regularly. We have a bunch more logos of the type others here describe that I could have chosen but that's dumb.
But the actual answer to your question of how is that it took a long time to build something they wanted to use. We've been building a version of Grain for about 15 months now, about 6 months on the product we just released and 9 months on a version we threw away.
Eventually we built up word or mouth of happy users that refer other teams. It's a grind to get real teams to adopt anything but it is possible with continued effort.
I guess we only have anecdotal evidence to go on here, but except for exactly one case I've always seen the organizations I work for get and wait for a positive response to their request before they display our logo. Does everyone else's experience really differ on this?
I have had exactly the same experience in my previous (and in my current) startup. I would never add the logo of a client without their consent. (maybe some don't follow that logic)