it should work.
"for use only as an upgrade to a qualifying hp windows 7 upgrade option pc." simply meant it was included when you bought specific select HP PC's.
It doesn't mean that the upgrade is limited to HP pc's .
I think if dell sent you the upgrade, they would give you a working CD. They don't want an unhappy customer
If it still doesn't work, have it sent back, like the lady said to you. Hopefully you have the name of the person who told you that info and the date and time when you called.