The fun part is that they do not understand what it means to have your "own datacentert" vs renting server in a co-lo. It does not matter if you are running on AWS on Hetzner it is somebody else's computer.
We were a similar sized company at about the same time - we owned our data centers in the same way we owned our offices - we leased and occupied them. Sure, if the plumbing sprouted a leak the landlord would come to in and fix it, but no one would be confused enough to say we didn’t have our own office space.
"The fun part is that they do not understand"
YES, 37Signals, I company with a legendary pedigree of pushing technical boundaries and open minded with deployment models totally doesn't know the simple thing that you do.