For them to share a space do both Ratfolks have to have the Trait? Because the wording doesn't exactly say both of them have to have it. I have a friend who took the Cornered Fury trait instead since he was the only Ratfolk and I made up a char that I could use if mine dies.
No you both have to have the trait for it to function correctly. Technically you could share his space, but since he cannot share your space it does not work.
Depending on your character classes, it might be worth having your friend take the Additional Traits feat in order to pick up swarming. It's a BIG help for Rogues, since they get to Sneak Attack whenever flanking, and count as flanking when swarming.
Additional traits lets you pick up more character traits, not more racial traits. So, that doesn't work. They really should have named these something different though.