I'm not sure what you mean here? There are Pathfinder home games, obviously, and they probably outnumber the Pathfinder Society games, but there were 3E home games and they probably outnumbered the Living Greyhawk games, no? What is the difference between Paizo's and WotC's approach you're thinking of?
Paizo's approach very clearly and very visibly doesn't rely on the rules as the centerpiece. While their products do support PFS and vice versa to a large degree, at least one major line, the APs, aren't used by PFS at all, and most of the supporting lines are timed to support the APs primarily (i.e. a companion book on a specific region that plays center stage in the current AP) with PFS working them and the later published hardback books into the PFS ruleset only as soon as the PFS coordinators are comfortable doing so. In the end, with all the products that Paizo has going at once, PFS ends up being just one way people can learn about and play the game, with the focus of the system actually being on supporting the world of Golarion, not PFS. Also, Paizo devs routinely either begin or end their forum posts with a disclaimer of some kind that DMs are free to do what they want, a message routinely pushed out by Paizo in all of their products as well. So far, at least to me, they have done a good job overall of managing the balance between DM fiat and player control of their own character. They also are very active in getting the word out in what their intentions were in their designs and interacting with the community about where both intent and execution could be improved.
With WotC's emphasis on rule splat books during both 3rd and 4th edition, few adventures, and world support beyond FR (and sometimes even FR) being sporadic, there ended up being less highly visible products to hook and retain new players beyond the rule books themselves. Add in the fact that Living Greyhawk (and later LFR and Encounters) had far more visibility than your average home game and new players tended to get a lot more reinforcement that the rules as written in the book were the only proper way to play. WotC also rarely in 3rd edition took the time to highlight the role of the DM being the final moderator anywhere in any of their products or dealings with the community, so even if they weren't actively discouraging DM rulings, they were also doing very little to discourage the growing sentiment of player entitlement during the time frame of the 3rd edition books. The rules, through a number of factors, were forced into a spotlight they were not designed to be in, and the system suffered as each splat book made that focus even more and more rigid. They tried to correct this with 4E, and ended up overcorrecting it and not correcting it at all at the same time. They pushed DM fiat as much as they could while publishing splat book after splat book that seemed to reinforce the player being the key controller. The net result was a lot of confusion on the part of the newer DMs and players, who for lack of a better option, usually ended up deferring to the written rules during 3E or simply not playing 4E because of the confusion.
They are doing better so far with 5E overall when it comes to that message, though, at least up to this point. They are pushing a reasonably clear system that both DMs and players can understand while making it clear that all rules are optional pending DM approval. Whether they can continue to support that will be the key determining factor of it's long term success. So far, it's doing a decent job, but not one likely to fully win back the majority of lapsed players. If it can continue on its present course, though, it will prove solid enough to sustain the brand and stop any more damage from happening.