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If they have PR7 or 8 sites linking to them, that will give them higher PR. There are many factors that influence PR, reading the Google Knowledge Base [webmasterworld.com] will help you with the basics.
I simply can not figure out how can their PR be awarded 7
Yes, you may have more backlinks, but might they have been lucky enough to get a few high PR backlinks? Have you taken a look to see where they are linked from? Is there a PR8 or PR9 somewhere in there?
There are dozens of other possibilities. Keyword density, keyword placement, title, page size, link anchor text, domain name..etc..etc..
Take a peek around their site, sooner or later you'll run across something.