I'm actually pretty inclined to agree, in the limited comparisons I can make. I have not played anything prior to 2e, being that it was when I started playing, but comparing it to 3/4/5 - I'm definitely going to agree.
Thanks to recommendations from these boards, I've recently bought the 1e material to go back in time, so to speak, and give it a whirl.
So, I'll explain my experiences - comparisons:
When I played 2e in the beginning (and when I even go back to it now) the groups tended to never make it past level 7 or so - the most grueling levels, in all honesty, with those terribly high-starting saves. Not to mention the 'cliche' (that is incredibly true) of cats being able to one-shot Wizards. So the fact we never really saw anything double digit matters, to my relative perception.
With 3E, we actually made it to level 20 in the very first campaign in which I participated. This was with the exact same DM, so style has little relevance. He always made up his own adventures, so what we have to look at is intent - did his intent change? Nope. Did the system's intent change? Most certainly. 3E was obviously written as the first step to overturn the 'DM vs. Player' mentality, and it worked sufficiently. Not only were my experiences in 3E far less deadly, but I believe that was a design intent.
With 4E, I never had a single character die - ever. I killed one, as a DM, once. The tactical-driven battle made it -feel- very deadly, though. With the right encounter makeup, and a good party, you could feel the threat of death without actually dying, which I have to give it credit for.
With 5E, I've actually had characters die a bit more often, probably moreso than 3E, but that has nothing to do with mechanics whatsoever, so we'll ignore that. I rarely feel the sense of threat like I did with 4E, or 2E when playing Fifth Edition. We've hacked and reverse-engineered half the mechanics to -make- it threatening, but RAW/RAI, as this discussion pertains to, I don't find it really worrisome at all.
So, a recapitulation - Died a lot in 2E and never broke level 7 - 9. Died incredibly rarely in 3E with the exact same DM and the exact same dastardly mentality. Didn't die at all in 4E, and I should practically say the same of 5E. This is, as always, obviously one person's perspective. It is my sincere belief that the deadliness, as written, has decreased from system to system on purpose. They leave it so that we the players can easily control the deadliness to our own desires, instead of having it written in the books - the first step of the multi-pronged attack that is eradicating the DM vs. Player mentality that pervaded the industry for a long, long time.