It's real, but only in the first and second editions.
(I don't have any electronic proof, but I've seen it in my copy of the second edition and someone else's copy of the first edition.) It's the only exercise in the chapter.
The full quote in the second edition is:
Take any book on homological algebra, and prove all the theorems without looking at the proofs given in that book.
Homological algebra was invented by Eilenberg-MacLane. General category theory (i. e. the theory of arrow-theoretic results) is generally known as abstract nonsense (the terminology is due to Steenrod).
If I'm not mistaken, the quote is the same in the first edition. First edition: page 105; Second edition: page 175; so you can look in your library to see if I messed up the quote!
And I do have an electronic copy of the third edition, which I've searched to confirm it is not there. The historical remarks were expanded, written less dismissively and put at the intro to Part Four.