Oh, yogawordmom, your story sounds so familiar!
So our school looks at the CogAT testing more as an "ability test screener" for all students, to decide whether further individual (although abbreviated) IQ testing is warranted. Hopefully, your principal will respond (and keep FERPA in your back pocket), but yes, usually you should be able to see those scores. Our schools are slow to share this type of information, too.
Our schools also require separate "achievement" data in their screening process for G&T. The CogAT doesn't count as "achievement data" for us, but perhaps other schools use it differently. MAP testing is actually the achievement data our school uses.
As the always wise polarbear has suggested - YES, if the school prefers certain testers, use them. In fact, we waited for the school to do its testing (with its own school testers) and waited for all of the results to come in (the school definitely takes its time with sharing its data with parents), before we decided to pursue some additional testing (by then, we had our own questions we wanted the answers to, so the extra testing was for us - she was already in the school's program). We will probably do things differently with child #2, because I think child #1 was probably neglected a bit too long while the school went through its long process to decide whether she was eligible for their programming.
Parents need to also trust their "gut" on these things - YOU are really the expert on your child!
Let us know how it goes with the principal. BTDT!