Sorry Shmendrick
As you often point out you have a trained and well honed Gemarokup, as such you should be able to understand the “chiluk”
The Gemora in Beitzah is giving a havtach to an individual, that individual should understand that he need not worry about his expenses on account of the money spent “L’Talmud Torah”.
However the Yeshivos are the ones charging the money they must charge the person according to what they see.
It so happens there is a “minhag” by some that they do not “bargain” over schar limud and the mekor for this minhag is the aforementioned Gemorah.
A slight point however is that when a portion of the “Schar Limud” goes towards secular education, one must understand that presumably the Havtacha is not for that portion of the tuition.