No, that doesn’t mean that. EFC is a misnomer…just something the feds made up. The feds can’t demand that schools give you aid up to that amount. In fact, most schools can’t give you any free money with an EFC of $10k.
Since your EFC is too high for a Pell Grant, your $10k EFC means nearly nothing, except that your child might get some work-study and a small subsidized student loan and a small unsub loan.
For example…let’s say that your child wants to go to an OOS public…let’s say Penn State which has an OOS COA of about $48k (don’t remember the exact, but let’s use this number).
Your aid pkg would very likely look like this:
$48k COA (cost of attendance)
$10k EFC
$38k is your “need”
FA awarded (BTW…FA isn’t just free money…it’s also loans & work study)
$5,500 student loan combo of sub and unsub loans
$2,000 work study
$7,500 total aid award
No free money
and you’d be gapped by about $30,000 which would likely mean that your child can’t attend.