Is "I don't have enough funding" the most popular phrase used as hint for rejection From communicating with fellow peers, it seems that whenever a professor rejects a student for graduate entrance, he or she will say something along the line of "sorry there isn't enough funding" or "our funding cannot cover a spot for you this year...but feel free to apply again".

This phrase also work its way into graduate interview as well, where the prof would suddenly mention funding questions, and thinks out loud whether he will have enough funding this year to take you.

While all the students failed to get acceptance offer when something along the line of this phrase is uttered...I wonder if there is a pattern in academia (applying for post-doc position, or research) where rejections are treated as lack of funding issues.
It is likely an amalgam of the truth and a gentle let-down. It's a polite way to reject someone, in that it doesn't place the failure in the hands of the applicant. There's nothing you technically did wrong. Nothing you necessarily could have changed. It just didn't work out.

It's also very likely a truthful reason for not accepting a candidate. It's possible that, given a couple more graduate funding spots (getting lucky with a grant, or promised a few TA spots for their students, etc.) that they might accept an additional student, but when those don't work out,  there's nothing for it.