Did you actually read the early decision agreement you (and your child) signed?
Here it is:
“If you are accepted under an Early Decision plan, you must promptly withdraw the applications submitted to other colleges and universities and make no additional applications to any other university in any country. If you are an Early Decision candidate and are seeking financial aid, you need not withdraw other applications until you have received notification about financial aid from the admitting Early Decision institution.*”
Unless I missed it, that agreement says nothing about the odds of ED admission being higher (in fact, most selective schools go out of their say to specifically say that it is NOT).
Now I happen to think that binding oneself to a committment to enroll when the institution has committed little in return other than an earlier decision date is not a great deal but that is the deal that many of us (myself included) took.