His first-choice centre-half pairing of Rio Ferdinand and Nemanja Vidic are struggling for form, so when an international defender says the United manager doesn't fancy him, it's going to raise some eyebrows.
Would Garay have had a better game than Ferdinand against West Brom last month? Probably.
But it doesn't mean Moyes has dropped a clanger by not signing Benfica's Argentina centre-half this summer.
When he replaced Sir Alex Ferguson, the centre of the defence was one of the few areas he found well-stocked.
Not many clubs have two international centre-halves to call on. However, in Ferdinand, Vidic, Jonny Evans, Chris Smalling and Phil Jones, United have five. Michael Keane and Tom Thorpe are also waiting in the wings.
If Moyes had spent £20m on another he would have been accused of wasting money that would be better used elsewhere.
His priority this summer was in central midfield, not centre-half.
More than that Moyes has shown a willingness to put his own stamp on the club he joined this summer.
Speculation linking Garay with a move to Old Trafford long pre-dates Moyes' appointment.
If the former Real Madrid man had arrived on Moyes' watch, it would have looked like Ferguson's influence reaching into the new man's era.
Almost as if the Chosen One couldn't choose his own players, but if Garay is to be believed, then Moyes has shown himself to be his own man.
And, as difficult as it is to replace the irreplaceable, that can only be good news for United.
The former Everton manager has said it may well be 18 months or even two years before he can put his mark on United.
It should only be expected after taking over from a man who was there for 26 years and won everything there is to win.
On the other hand, different managers like different players, and if Moyes has pulled the plug on Garay, then that's something to be admired.
He's made the first tentative steps in moulding United in his image with the signing of Marouane Fellaini from Everton.
United fans haven't seen the best of the Belgian midfielder yet, but it will encourage them that Moyes has not been content to simply hold the rudder.
He's shown the ambition to take United to another level.
Whether he achieves it or not is another matter, but Moyes has at least demonstrated the guts to try.