The reason for your problem is the command evaluation process in ksh. You might want to read what i have written for a different (but related) problem here.

Your commandline is first interpreted locally and the content of the variable is filled in and protected by the double quotes. Now a remote connection is opened and the rest of the line is passed as command line to the remote shell interpreter. Guess what? At the remote site the commandline is getting interpreted *again* and now the double quotes are not there any more because they are already "used". The command will look like this (first line=local, second line=remote):

rsh host grep ^Sat Jun 13 06:19:07 CEST 2009 file
              --------one argument-----
grep ^Sat Jun 13 06:19:07 CEST 2009 file

rsh host grep "\"$xx\"" file