Yes they are the same socket, both processors are 1366. My guess is probably for whatever reason thier proprietary motherboard doesn't support the upgrade. Usually OEM computers are very limited in what can be upgraded. If the motherboard doesn't support the 960 you would have to get a new motherboard which means new RAM and of course the processor. That right ther is half the computer that's why the tech said it would be easier to just get a new computer. Also have you gone onto Dells website and checked the CPU compatability list of your computer just to make sure what the tech said is right?
Customers looking for a bit more power can certainly find it; the quad-core Core i7-960 will run an additional $470 and the six-core Core i7-980X upgrade is a cool grand.
They are probably unable to reference the correct documentation and trying to sell you a new computer. I have upgraded CPUs in a number of Dell XPS machines without a problem, staying in the same processor family. Dell is rather good (historically) at providing BIOS compatibility for CPUs.