I have not used xarchiver before, but most graphical archive/unarchive programs in Linux use the respective command line tools for each archive type to perform the compression or extraction. In Debian Wheezy xarchiver merely suggests the rar package because xarchiver is in main but rar is in non-free. Therefore you probably do not have the unrar package installed on the machine that fails to open the archive. Other graphical archive programs should exhibit similar behavior to xarchiver because they all rely on the proprietary rar software to extract that archive type.
$ aptitude show xarchiver
State: not installed
Maintainer: Christian Hübschi <firstname.lastname@example.org>
Uncompressed Size: 1,523 k
Depends: libatk1.0-0 (>= 1.12.4), libc6 (>= 2.3), libcairo2 (>= 1.2.4), libfontconfig1 (>= 2.9.0), libfreetype6 (>= 2.2.1), libgdk-pixbuf2.0-0 (>= 2.22.0), libglib2.0-0 (>=
2.14.0), libgtk2.0-0 (>= 2.10.0), libpango1.0-0 (>= 1.14.0)
Recommends: xdg-utils, arj, bzip2, rpm, p7zip-full, unzip, zip
Suggests: lha, rar
Description: GTK+ frontend for most used compression formats
Xarchiver is a Desktop Environment independent GTK+ 2 frontend for manipulating 7z, arj, bzip2, gzip, rar, tar, zip, and RPM files. It allows you to create archives and add,
extract, and delete files from them. Password protected archives in the arj, 7z, rar, and zip formats are supported.
You should either install rar and unrar or install xarchiver with all suggested packages. Running both of the commands below would not hurt, but you only need one or the other (as long as xarchiver is already installed, otherwise you need the second).
$ sudo apt-get install rar unrar
$ sudo apt-get install --install-suggests xarchiver