I dunno, there might be something in that.
Our natural body chemistry changes over time and perhaps there is a change which is beneficial which begins at or around the age of 40.
I say that because approaching that age myself I underwent a drastic body chemistry change, (deliberate and self-inflicted), which in the space of a few weeks saw me change from someone who used to become extremely breathless wiping their own backside so broken was my cardiovascular system, to someone who had no problem cycling for a dozen miles at an average speed not far off 30mph.
I'm serious by the way, I genuinely had to rest between wiping my bottom and washing my hands because of my cardiovascular issues and I really went from that to a few week later cycling a dozen miles at just under 30mph average speed with zero fatigue and zero breathlessness, (when I pulled my phone out of my pocket I genuinely thought my GPS app was playing up because of how far it was telling me I'd cycled and how quickly I'd done it, then I pulled up the map and it highlighted my route with 100% accuracy).
I'm not saying that is precisely what happens, each persons body chemistry is different and what I did to myself is in no way at all natural, not even close, but maybe there's a gradual change which brings gradually more benefits and that's why the saying persists?
I don't know, I'm just hypothesizing, there's very little study done on stuff like this when you think about it, maybe I'm way off base, maybe I'm bang on.
Either way, I certainly wouldn't rule it out based on what I experienced when I became my own scientific Guinea pig, lol