While this is complete conjecture, I don't think the ability to ascertain truth from falsehood is uniquely age related; I believe it comes down to the age of media you were raised in. That's not to say it age doesn't play a factor at all, as cognitive function does decline as you get older. Unfortunately we don't have the data to control for generational changes, so 'older people' and 'the current older generation' are used synonymously. In my opinion, younger generations have become better accustomed to the bombardment of lies, in the form of new age marketing, that older generations didn't have growing up (at least, weren't as acutely aware of). That is compounded with the fact that people become more trusting of their chosen form of media over time [1]. If you've grown up with a small amount of media to choose from, and develop a loyalty to a certain one, it's a hard cycle to break out of.
Anecdotally, it seems to me that the older people I know only consume information from 1-3 sources, whereas younger people tend to flip-flop between many different ones. So if any of that small pool of media sources becomes untrustworthy it 'poisons the water', so to speak, much quicker.
To add to this, modern forms of media often have instant feedback mechanics (article comments, suggested counter-articles, up-vote/down-vote functions etc.) that can control fake news to a small extent. If someone shares fake news on HN for example, I can read the discussion and be made aware of any falsehood in the article. Traditional paper and television media does not have this control mechanism. Take note, I'd argue that this argument shouldn't apply to Facebook (which happens to be the most used website for over 50's). Their algorithm favours popularity over anything else so even if people react negatively to it (angry react), it only serves to spread fake news further.
[1] https://www.americanpressinstitute.org/publications/reports/...