No, it is not. Those who say it is correct do not know how to parse a sentence. What it comes down to is determining what is modified by the relative clause - the part from 'that' on. In this construction, it modifies 'schools', so the relative pronoun 'that' is plural and the clause requires a plural verb - place.
Breaking the sentence into two simple sentences instead of a complex sentence with a relative clause shows this.
Few schools place great emphasis on both subjects.
MSJ is one of the few.
How would you write it to have the clause modify MSJ and still make sense?
MSJ, which places great emphasis on both subjects, is one of the few.
That is a grammatically correct sentence and might even be used in a conversation. But notice the clause is set off by commas whereas your sentence (correctly) had no commas. Essential clause have no commas; nonessential do.The clause modifying MSJ is nonessential, so it is set off by commas. It is nonessential because there is only one MSJ - the clause just provides extra information and is not essential to determine what MSJ is, so you use commas.
Moving back to the original sentence, there is no comma because the clause is essential. 'Few schools' could be any combination of two or more schools. What is essential to define those 'few schools'? It's the clause. Since it is essential, it is not set off by commas.
That's a pretty long-winded explanation. I don't mean to be boring, but when that many post erroneous answers a more detailed reply seems in order.