I see no reason why not. Your motherboard has a PCIe slots where the 6670 could go. http://h10025.www1.hp.com/ewfrf/wc/document?lc=en&dlc=en&cc=us&docname=c00906137#N272
The only reason that they will say that is either because your case is slim or the power supply is not enough. Unfortunately, both information can not be derived from the web. Can you confirm what is your power supply? How many watts?
And whether your case is the slim type ( around 4" wide ) or at least 6" wide?