Bottom line: "every" full time student under 24 is claimed by his parents, because it's usually the smart thing to do.
But, if you're concerned with being technically in compliance, the support work sheet "is the thing". It is what the IRS will ask for (in the unlikely case that they ask at all). Most people just use estimates (or these days accounting software like Quicken) and not receipts.
I'm surprised at your low $700 estimate of what you parents will lose. The American Opportunity tuition credit (AOTC)*, alone, is $1000+.
The interesting thing is that if you tried to claim that $1000, it would be a red flag to the IRS (assuming you're an undergrad, under age 24). So, there is less chance of an audit if your parents claim you, rather than you claiming yourself and the tuition credit.
*A full time unmarried student, under age 24, is only eligible for the refundable portion (up to $1000) of the American Opportunity Credit if he supports himself by working. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants. It is usually best if the parent claims that credit.
You cannot claim a credit if you are, or can be, claimed as a dependent by someone else.
