OTOH, there is just correlation in an otherwise minimal article. The only support, two very similar articles, is pure correlation, and both are based on all adults, not just elderly. The jump to "it lengthens your life" is made on a single quote.
If someone ever brings me evidence that having stronger grip does not help you avoid falls, then (a) that would be surprising and interesting, and (b) I wouldn't feel like a fool for having improved my grip strength anyway.
Empirically proving causation is often difficult or impossible. It's irrational to expect every potentially useful idea to meet that high bar before taking it into consideration. If someone is trying to sell me something, or if the idea goes against common sense, I'll demand proof, but that's not the case here.