Nike was definitely one of the big "head-to-toe" companies, but so was TaylorMade/Adidas, Titleist/FootJoy/Cameron/Vokey and Callaway/Odyssey. It wasn't unusual for player's contracts to stipulate that they play 12 or 13 clubs from that manufacturer plus the ball, and wear the clothing, shoes, glove and headwear as well. There were exceptions, but companies wanted "the count" in all the categories for the Darrell Survey.
There are just some clubs that are more private than others. One that comes to mind is Preston Trail in Dallas.
I did an event there about 10 years ago which was almost a total bust because unbeknownst to us the course was closed for renovations, and only the driving range was open. It was pretty much a ghost town. We had a lot of time to kill and talked with one of the assistant pros for a while, and he explained that because the course was going to be closed for an extended length of time, they had to buy memberships at other clubs in the area so their members would have a place to play. Many of the members there belong to more than one club, but for those who didn't they actually purchased memberships at other private facilities, which they had to because they don't reciprocate with other clubs. I thought that was interesting.