Thanks Tolkien. Here's where I get stuck. And perhaps this is as simple as "Robert doesn't understand breakthrough infections" but here goes.
From everything I've heard and read, you're not a big transmission risk with a breakthrough infection. I just googled to find something recent, and here's an article from NPR on the topic last month (LINK). That seems to indicate there's a very small chance someone with a breakthrough infection could give the virus to someone else.
I can maybe understand some caution in accepting that as 100% fact until there are months of studies done, but here we're talking about a vaccinated person (BB) who is likely not contagious banned from a building full of 100% vaccinated people because there's a tiny chance that he could give one of them a breakthrough case followed by the even tinier chance that they too would be contagious and they might give someone else the virus. Aren't we reaching "less than a 0.1% chance" or something close to that?