Well it looks like I'm late to the water cooler as usual...
My two cents: Any game can be customized, but the writing of the game is a key factor in informing the culture that surrounds that game, and the culture of the game does a lot to encourage or discourage things like customization, tinkering and house-ruling among groups.
2E had a culture generally amenable to such customization, probably due to a confluence of factors--the vast array of options produced that were often mutually contradictory, the tone of the books, the inconsistency of the system and the need (both real and perceived) to fix or stretch it.
3E, though I have less familiarity with its culture, seems to place more emphasis on sticking to the books--not necessarily so much within the game itself as within the larger game culture. This is the edition, after all, where RAW became a catchphrase.
I agree, for the most part. Unlike many of the previous posters I started my D&D path with 3e, although I have read a fair chunk of older material I've stumbled across. 3e may not have explicitly encouraged customization and houseruling, but it was widely acknowledged that if some part of the rules wasn't working for you or if your game needed different/additional rules that you should feel free to make changes. It was also acknowledged that you tinkered at your own risk because a lot of houserules came with unintended consequences.
With 4e though, it's become common, if not popular, to tell DMs they
shouldn't make houserules. I've seen countless threads where the OP mentions a problem with a certain aspect of 4e only to be told they should find a different game because they clearly don't want to play D&D. DMs who want to create a unique campaign that's significantly different from the average, default 4e experience are left with little to no support. Sure you can change Monsters/Skill Challenges/Powers as much as you like to get a tailored
encounter as long as you don't alter anything that effects the entire game. It's become implied that houseruling is bad - it's implied in the language the fans use to discuss the game; 'solid foundation', 'good balance', 'DMs are free to design encounters'. For myself, reflavoring is not a sufficient tool to customize my 4e experiences.
As for whether the OGL encouraged customization - I think it did, just indirectly. With so many alternative rules from 3pp, it precluded the need to create personal houserules for some groups and I don't think that was a problem. If a group found a set of (presumably playtested) rules in a 3rd party book that enhanced their game, so much the better. For those that didn't find perfect rules already created, I'm sure much of the material served as a jumping off point for many people. The GSL, on the other hand, restricts those opportunities greatly. Wotc is the only ones who can tweak 4e mechanics, which means no 3rd parties assisting niche groups looking for something different. I've also heard speculation that Wotc has no intention of ever offering tweaks and alternatives because it goes against their 'everything is core' policy. I'm disappointed that such speculation seems entirely plausible. A 4e Unearthed Arcarna is the most likely book to get me excited about running a campaign, but it would be relatively useless in the current Living Campaign designed market.