That's what I thought too, but upon testing it seems that PS1 is somehow 
special in this regard:

fs@zhenghe ~/tmp $ export $FOO=bar
fs@zhenghe ~/tmp $ echo $PS1
\[\033[01;32m\]\u@\h\[\033[01;34m\] \w $\[\033[00m\]
fs@zhenghe ~/tmp $ cat ps1test
echo PS1 in this script is $PS1
PS1="foo $PS1" bash -c 'echo PS1 in another shell called from this script 
is $PS1'
fs@zhenghe ~/tmp $ cat footest
echo FOO in this script is $FOO
FOO="foo $FOO" bash -c 'echo FOO in another shell called from this script 
is $FOO'
fs@zhenghe ~/tmp $ ./footest 
FOO in this script is bar
FOO in another shell called from this script is foo bar
fs@zhenghe ~/tmp $ ./ps1test 
PS1 in this script is
PS1 in another shell called from this script is
fs@zhenghe ~/tmp $ export PS1
fs@zhenghe ~/tmp $ ./ps1test 
PS1 in this script is
PS1 in another shell called from this script is
fs@zhenghe ~/tmp $ PS1="$PS1" ./ps1test 
PS1 in this script is
PS1 in another shell called from this script is
fs@zhenghe ~/tmp $ 

(Please forgive any horrendously deprecated syntax I might have used above, 
I don't know much about shell :) )

-Keshav

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