I can get a mortgage out for a house just fine, but I can't get a card, go figure

The reason why (and I just got a letter explaining this) is because my credit history is too short, but that makes no sense because everyone I know got a plain ol' credit card just fine. I have a house payment AND a home improvement loan that I pay on time and more than what's needed.
The whole credit system is a joke, if you ask me. But anyway..
The HELOC seems to be the best way to go so far as interest rates are between 3% - 7% (from the banks I've called), and they even pay all the fees (appraisal, title, etc..).
I'd much rather pay 7% (hell, I'd rather even pay 9%!) than the standard 16-21% that most credit cards offer.