The cynic in me always wonders "How many of the outlets that gave it GotY paid for the game and didn't get comped a review copy?"
Honestly, probably few or none. If this was actually a thing that happened a lot, then it would have inevitably leaked. All these GOTYs (and DAI) hit right around peak gamergate idiocy.
I think the simplest answer is that lots of people actually liked it.
Early review copies for major gaming news outlets are quite common, no? I think there's plenty of reason to be cynical of the mutual relationship between major game publishers and major reviewers.
But, I would presume that any reviewer getting an early review copy of DAI also got earlier review copies of many, if not most, other games. Sure, the press gets a lot of perks, and they get buddy-buddy with the developers at big events, and this definitely influences coverage, previews, and reviews to some degree. But all things being equal between publishers, this wouldn't really give DAI much of an upper hand in winning so many Game of the Year awards.
Despite how much I really like Inquisition, I'm actually pretty willing to buy into the narrative that the competition just wasn't as strong in 2014. But, even then, with the sheer number of GOTYs the game received, reviewers, as a whole, still must have thought the game was, at very least, really good.
Whether one thinks these reviewers' opinions are worth anything is their own prerogative, but the narrative that DAI's GOTY awards were all, or even mostly, bought or lobbied just doesn't hold much ground. Even less ground considering past big GOTY winners were The Walking Dead and Journey.