Another great suggestion! 
It turns out that posh-git is setting a HOME environment variable to the bare C:\users\davidski directory. This environment variable is normally unset (Windows uses HOMEDRIVE and HOMEPATH). When set, this causes tilde expansion in R to go to C:\users\davidski instead of C:\users\davidski\Documents, the later of which is what I get for tilde expansion when starting RStudio "normally." Interestingly, bare tilde expansion directly in cmd.exe or powershell.exe CLIs with $HOME unset gives me the C:\users\davidski path and not the Documents subpath.
Reading through the Startup help, I'm not certain which flavor of tilde expansion (the bare user directory or the Documents subdirectory) is considered normal for Windows users. Documents seems like an odd location for dotfiles such as .Rprofile and .Renviron, but I can't see how vanilla Windows installations would default to anything besides the user's Documents folder.