I agree with this. It wasn't just Sony's hype, it was the fact that literally everyone on Earth seemed to accept every single rumor or exaggeration about the PS2's capabilities as fact and took it from there, spreading the hype more effectively than Sony could have ever done alone.
I will disagree, however, with the point you made suggesting that the DVD player wasn't such a strong part of its initial success. DVD player prices dropped drastically after the release of the PS2, but before its release, most players cost at least $200, and a decent one (such as a Sony) was $250 or so. Considering that DVD players had not yet reached market saturation at that point, a whole lot of people were purchasing the PS2 as their first-ever DVD Player, and for just an extra $50 they got a state-of-the-art (or so everyone and their mother was saying) game system as well. Bargain.
Or to look at it another way, they bought a $300 system (standard) and got a 100% free DVD player in the process. Again, bargain.
Edit: I got paranoid that perhaps I was remembering incorrectly, but no, it seems I was OK. This is a Comp USA flyer from around the same time. The PS2 launched in the USA on October 26, 2000. You can see in the ad that NFL Gameday 2001 for the PlayStation is advertised, which was released on October 30, 2000. And the Toshiba standalone DVD player on the same page is $250.