@arjun sir, I think she has given the perfect answer. If the K is also an input then also it will take only $k.log n$ time (maximum will be $n.log n$ time), which is definitely less than quicksort $k.n$ times (maximum will be $n^2$ times. .
And actually this is a very famous interview problem, and she has stated the perfect solution. Which is suggested by some of the best profs.
And you have suggested the Kth largest number algorithm, It perform real bad if K is very less. And its theoretically seems that perform better than heap method but its not a huge improvement. Its similar to strassen Matrix multiplication over general algorithm, covert 8 multiplication and 4 addition into 7 multiplication and 17 addition and shows some 0.19 improvement..