It is a very fine line but this part is probably not true. She's 4 years old and doesn't need to learn to swim, unless you really want an Olympic swimmer.
If she keeps going swimming in the shallow end, do you know what will happen? She will get bored and want different things (including deeper water).
I see this kind of thing frequently, kids work at a slower rhythm than parents and parents are still human and have limited time and patience.