I've heard people complain about the tuning stability of this model guitar before but I've always ignored it as my first experience was a 25th Anniversary Custom 24 that simply never goes out of tune.
This is my experience with my Greg Bennett D5 acoustic. I thought last night that I'd better check it with the tuner and with the exception of the B string everything was spot-on. The B string was a bugger to tune in though so I am assuming it's something to do with the nut. I might need to put some lubricant on the nut. Otherwise it was perfect! It has Grovers. It also still has its original strings (might need changing by now), so no issues introduced by a bad stringing job on my part.
My SG goes out of tune a lot now since it was restrung when I installed the BKPs. I tend to think this is because the strings have been backed off a lot twice since then when removing the bridge for various reasons, rather than it being the fault of the strings or the original stringing job I did. Again this might in part be some kind of issue with the nut, but it might also involve the interaction between some kind of kinking (maybe mild) of the strings causing issues either with the tuners or the nut. It has Klusons.
My Explorer goes out of tune nearly as much as the SG. Not sure why, but it could be a couple of reasons. I've always had issues with the B string on that guitar. Could be the headstock design, or again it could be an issue with the nut. Also I installed 'Skinny Top, Heavy Bottom' strings on it without enlarging the slots in the nut for the E, A, & D strings. They might be okay but they might also be a little tight. It has Grovers. I used to get a 'ping' on the B string before I changed strings last time but I suspect that might have been something to do with the nut rather than the tuner as changing strings seems to have fixed it.
I would look at the nut before changing things around ...