Is the phrase "make the grade" correctly used in this context?

I was interested in the following sentence which appeared in an article titled “How My Child Skipped the State Tests" by Robert Kulesz in The New York Times, School Book, (May 9, 2012).

To be fair, I’m sure she felt she acted in the best interest of her school, given Mayor Michael R. Bloomberg’s insatiable desire to shut down public schools if they fail to “make the grade.” [note that the double quotation marks are of the journalist, NOT MINE]

Can someone clarify if the idiom, or idiomatic phrase, "make the grade" is correctly used?

I have found (The Free Dictionary) the below meanings for this phrase, but no one is referred to academic grading:

• to be satisfactory; to be what is expected.
  I'm sorry, but your work doesn't exactly make the grade. This meal doesn't just make the grade. It is excellent.
  McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.

• to succeed at something, usually because your skills are good enough (often negative).
  He wanted to get into medical school but he failed to make the grade.
  Cambridge Idioms Dictionary, 2nd ed. Copyright © Cambridge University Press 2006.

• to be good enough An excuse like “
  I didn't call because I couldn't find your number†doesn't make the grade for most women.
  Cambridge Dictionary of American Idioms Copyright © Cambridge University Press 2003.

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Solution 1:

To make the grade simply means to meet some standard set. It does not refer to academic grading. The quote involving the public schools simply refers to whether they meet the standard or not.