I'd say false - I loaded mine Dell branded disc of XP Home onto my Compaq machine, tho I did use the Compaq licence (from the sticker on the side of the case)
If it is a Dell badged XP install disc then as suggested above you should be able to install it on any PC.
If however it is a Dell recovery CD then it will only work on the Dell PC that it was intended for - and not even another Dell model (probably).