I have a problem with the idea that "Nothing is fun until you're good at it." Whatever happened to enjoying a challenge? My son doesn't like math because it is easy for him - he likes it because we have taught him to embrace challenges in life rather than run from them. As a result, he's almost three full grades ahead in math. Meanwhile, he HAS been in school plays, does NOT know how to play an instrument (he has asked about playing the guitar - not the violin or piano - and I'll probably let him do that soon if he is still interested), plays baseball, and most of all, HAS FUN. That's what a little boy is supposed to do. Having grown up in a household that was not quite as strict as the one she described, but had some striking similarities, I firmly believe that the most important thing is for children to know they are loved even if they screw up. Yes, they should be pushed to do their best. But they should never be made to feel like a show dog who only receives love as long as they are bringing home the trophies.
There is some merit to this - kids don't need as much free play time as some parents seem to think they do. (It's been my experience that BOTH of my children are better behaved when they have organized activities on a regular basis). But it is important that they have SOME free time.