I most certainly am not.
I don't have time to run the numbers, but the numbers I already stated are for a full third of the population, but the number goes up considering that there is a large number of people for whom 2001 would constitute either their very first memories, some of their earliest memories, or a part of their childhood. Unless you're idk 10, memories from your childhood are certainly seen as being from a different time.
In 2001 DeviantArt was just beginning to gain users. Wikipedia was just launched. We just upgraded to IE 6 and visitted YTMND. Friendster and Meetup did not exist. AWS wouldn't exist until next year. Firefox, Myspace, Youtube, Facebook, Orkut, Flickr, Gmail, Digg, Reddit, Vimeo...Hell, Club Penguin was still in our future.
We were still doing cultural damage control on the Y2K bug. The Motorola RAZR, certainly a socio-historical landmark, wouldn't exist for another 3 years. The very first iPod wasn't released until the end of the year.
I really don't think you could find a single person that can not see that the web of '01 was an objectively demonstrably different thing as compared to the web of '26. In rereading the original comment, I can see perhaps that the argument is that perhaps '01 is not "the early internet" given that by '01 the "bubble had popped", but that's kind of silly given that "early" does not in anyway mean "original". Like the "early bronze age" doesn't mean "the first time someone forged bronze". The same will be said of '26 in '46 when talking about the "early LLM days".