Yes, people actually are claiming that these new NNet advancements are the key that will unlock AGI, which by its very nature implies that they will be as advanced, or more advanced, than humans in all forms of intelligence.
Who are "people" in this context? Are you talking about the general public, or misinformed journalists who are writing about things they don't understand? Because from what I've seen, by and large, the researchers working on Deep Learning are not claiming that DL (alone) is sufficient to achieve AGI, nor do they posit that AGI is anywhere close to reality. Read, for example, Martin Ford's book Architects of Intelligence[1] and note how the various researchers interviewed talk about AGI. That list, BTW, includes all three of LeCun, Hinton, and Bengio, as well as many others.
Let's use a concrete example of technology being overpromised to the public - self-driving cars. Now there is some debate as to whether or not general AI needs to be invented in order to make self-driving cars a reality, but I don't want to dive too deeply into that. One thing that's obvious is that self-driving cars have already been promised to the public (Waymo claims to have launched last year but it's really just a private beta with a handful of users). Cruise is supposed to launch a public service this year in SF. Zoox is supposed to do the same in 2020 (and in custom built cars, no less). And there's no doubt that machine learning plays a critical role in the advancement of self-driving cars.
Now if you talk to the actual researchers/engineers when they're not afraid of hiding behind their NDAs (basically a friend at a bar), these people will talk about the challenges and how much work there is to do and so on. But the company's public stance, and the many billions of dollars chasing this area, is that it's just around the corner.
The point is, there is a lot of hype and it's easy to understand why. Elon Musk is happy to proclaim that Tesla is already selling the hardware for full self-driving vehicles, and it's just the regulators holding him back (which is absurd, to put it kindly). This is the same person saying AI is a bigger threat than nuclear weapons. So arguably the largest tech celebrity isn't even talking about when, he's saying it's here and we need to be prepared. This is the kind of person shaping the public's opinion.
But the money chasing these investments are mostly from private VC firms and tech companies, not public research grants. Once investors realize AI just isn't good enough for self-driving cars right now they won't want to keep throwing billions of dollars behind it. And that's when we arrive at a winter. Even Alphabet is starting to get weird about raising its stock price, so not even the tech giants are immune from this.
There are many other verticals that follow the same story, I was just using the most obvious example of an industry that has billions flowing into it despite nobody having a real product on the promise of advancements in AI and "the time is now!" But eventually (my guess is next year, but I'm old enough to know it's impossible to time these things) the hype will come crashing down to reality and that is when funding will dry up.
Who are "people" in this context? Are you talking about the general public, or misinformed journalists who are writing about things they don't understand? Because from what I've seen, by and large, the researchers working on Deep Learning are not claiming that DL (alone) is sufficient to achieve AGI, nor do they posit that AGI is anywhere close to reality. Read, for example, Martin Ford's book Architects of Intelligence[1] and note how the various researchers interviewed talk about AGI. That list, BTW, includes all three of LeCun, Hinton, and Bengio, as well as many others.
[1]: http://book.mfordfuture.com/