That makes sense. The weird part to me is that Homebrew would limit their approach and eliminate an entire class of use cases to accommodate programs that work this way. There has to be more to it.
So, based on the responses from the maintainers, for the .linuxbrew directory to be used, you have to satisfy 2 conditions:
1. you have to be installing one of the ~10% of formula that isn't trivially relocatable.
2. you have to be using a precompiled binary (which it seems like homebrew is smart enough to not do if condition #1 fails and you're not using sudo)