Morkus from Orkus
I'm unaware of any such text in the 1e PHB, and I can almost quote the darned thing. Beyond that, getting 2 15's out of 6 rolls of 3d6 is actually fairly unusual. You'd have to allow at least 6 or more rerolls for most players to manage that. Nobody in my experience was doing that, although the DMG methods considerably change the odds. 1 in 3 characters using method II will have 2 15s. Method III will AVERAGE 3 15s, and Method IV should produce roughly 2 sets of stats with 2 15s. I'm not sure about method 1 exactly, I don't have dice calculator I feel like playing with to get that one, but IME 2 15s using Method I is similar to Method II. Note that not all these methods let you pick WHICH stats the 15s will be in, assuming you get them. Method III was widely considered too generous, but nice for rolling up higher level PCs (which tend to be the ones with better stats if you played them out).
Again though, no hint of this exists in PHB. I think its safe to say that the DMG tells us Gygax WAS aware of the problem, and was interested in giving players something more like what they wanted. Truthfully ability scores in OD&D pre-Greyhawk were of marginal mechanical use anyway, so he probably just didn't think it was an issue back then. It was only with the advent of Greyhawk and then the codification of stat bonuses into 1e along with the 'advanced' classes that the issue really became acute. DMG helps relieve it some, but paladins were still RARE IME.
If you think no hint exists and are unaware of any such text, you need to read page 9 under Character Abilities. Unless you think Gygax was a complete ass was taunting people by giving them 3d6 and then saying, it's usually essential to have two 15's or higher BUT HAHAHHAHA!!! YOU'RE STUCK LOSERS!, then his saying that was a statement to the DMs implying that they allow players to re-roll until they got two 15's or higher. He himself was quoted saying that he ran his own games that way, coming up with alternative methods and allowing re-rolls in order for players to have sufficient stats to have a chance to survive.
Look, I played from 1975 until the end of 2e classic D&D. In the early 1e days I was in a gaming club that had 300+ members. We played D&D sometimes continuously for a week at a time with rotating DMs even. I saw plenty of it. Characters were nothing. They died left, right, center, up, down, and all around. If you made 6th level that was rare. There were some 'easy' DMs of course, but mostly nobody even bothered to name a character at level 1, or just called it by some generic name, or maybe it was a new guy and he named his character, which we thought was funny. Usually after a session or so the character's got some kind of nickname or whatever. That's just how it was back then. Maybe where you played everyone was gung-ho to RP every character fully and the DMs let them all live, I dunno.
I played from 1983 to the end of 2e and barely saw it. Since we had two very different experiences, this cannot be a game issue, or we both would have experienced the "inevitable". Rather, this is purely a player thing. Some players will act that way and others won't.