I believe that the man page for "cd" says it all.
The variable $HOME controls where you go when you type "cd" <enter>. NOT the $PWD variable.
If you change the variable HOME to HOME=/root for instance, your new "home" directory for root will be "/root" not "/".
NAME
cd - change working directory
SYNOPSIS
cd [directory]
DESCRIPTION
If directory is not specified, the value of shell parameter HOME is
used as the new working directory. If directory specifies a complete
path starting with /, ., .., directory becomes the new working
directory. If neither case applies, cd tries to find the designated
directory relative to one of the paths specified by the CDPATH shell
variable. CDPATH has the same syntax as, and similar semantics to,
the PATH shell variable. cd must have execute (search) permission in directory.