I feel for you and for her....it must suck interviewing a confident student who seemed qualified only to have her not meet your needs. But believe me, she is falling hard right now realizing everything that she doesn't know.
All cooking schools are great for giving controlled exposure to techniques and kitchen equipment. This builds confidence.
But I learned that there are a LOT of drawbacks to cooking school too.
1) schools do not allow for repetition, and the one chance you get at making something is usually ideal circumstances. You make a hollandaise once, and that's it! You don't learn how to do it over different types of heat sources....you don't learn what to do when it breaks....you don't learn to do it at kitchen speed...you don't learn the simple way of doing it (i.e. you learn a method that is fancy and more complex than most restaurants would use)...you don't learn many (if any) of the signs to look for to make sure you are on the right track. I could make hollandaise at home, no problem....but for the life of me, I could not make it consistently on a french top in a prof. kitchen with no double boiler.
She probably did the first cake just fine because for whatever reason, it was the perfect set of circumstances for her....but the next cake with the crumb problem, maybe the cake was drier, or the icing thicker...and she probably never had the chance to learn how to "see" these issues nor how to compensate for them, nor how to prevent them. She probably didn't even realize that she was doing it wrong until it as pointed out to her.
2) Students really are at the mercy of the teachers they get. My basic cookery teacher couldn't make a hollandaise herself....she tried and it failed. So she had us watch a demo by another chef and then never gave us the chance to make it ourselves......since I "knew" how to make it at home, I felt fine in bypassing the sauce. But WOW did this lack of knowledge show through once I was on the line.
And for that...I wonder if your new hire even ever received exposure to thickening using corn starch. To you, it is the simplest thing in the world to do, but I would not be surprised if her instructor taught them "If you need to thicken something....do it THIS way! THIS way is the best way....if you do it like me, you won't need to know any other way." (I have seen this before too.) And, she probably only thickened fruit a few times in total....each time she probably did it the exact same way as the instructor had taught them.
3) As for multiplying the recipes....wow....that is really bad unless, of course, they received all their recipes pre-multiplied for them. That was the one thing we DID receive repetition on! We were to type up recipes cards each week and adjust the recipes for the number of servings needed (actually, I think I did this on my own because I wanted to learn how to do it.) Either way, I am certain that she should have at least learned that much. So don't know what to tell you there.
I know the chef I externed under for a short time had a controlled-contempt for cooking schools for these reasons above (and more.)
But from the student point of view "How do I get into a kitchen without experience?" Cooking schools make you think you have experience....and let's be a little honest here....would you have hired her if she came to you with no experience but said she really wanted to learn how to bake?
Sadly, I do think that both sides get the short end of the stick on this one. She's led to believe she is ready for the big time....you know she is just starting out, but you didn't realize that YOU would be responsible for re-training her from square-one.
Man, I don't know if I really added anything to this discussion other than to say I am sorry for what you are going through. Good luck to you both!