While I agree with pretty much everything in Bookworms post, I will throw an unpopular opinion out there....
When the coach said "she's not ready yet" that could be exactly what he means.
He said she needed work on her form. It doesn't really matter how long a kid has been in gymnastics, some kids can come in off the street and be practically ready for pre-team and some can spend years in rec and never be team material. Just the hard truth of it.
I would (if finances allow it) let her do the two rec classes/wk for a while and see what the HC says in 5wks. At this point, you are either in the actual season already or heading into it. Another 5 wks would leave you no worse off as far as entering a program, because for most gyms the ship for this year's season has sailed regardless (hope that made sense). We do the spring season and do not accept any new competing kids (with perhaps the exception of someone already competing and moving to our area) after August. Any later than that, and you go in our pre-team, with the potential to go straight into L4 IF you have the necessary skills by spring next year.
Now, as a coach, I do actively scout the advanced rec classes for kids to move to either pre-team or team. We have two different tracks at our gym, the older, advanced rec kids with potential go into pre-team/L3 working group, the younger kids with potential go into our separate fast track group where we work much more conditioning and form. The kids going through that program tend to go straight into L4 when they are old enough. Not all, some go to L3. At 7 a kid isn't too old to join the pre-team/L3 group at all, we have kids up to 11 in it... But she would be on the cusp of being too old for the fast track group, it would entirely depend on where her form and skills were at.
I evaluate kids all the time for our pre-team programs and I'm always honest with parents when I tell them "she's not ready yet". For some, I can give them specific things I want to see improvement in, with a time frame (usually 3-6mo), and with the sincere suggestion that they come see me again in said time frame.
Others I simply tell they need to work more on their strength and skills and to remain in rec for the time being. I will take candid looks at those kids again, but not for some time (probably in the 6mo range) and if they haven't improved to where we need them to be, I don't suggest to the parents that they try out again.