The point surely is that what constitutes 'old' in most people's minds has changed as time has passed. In the 1950s, say, one's granny aged 60 was probably an 'old' wrinkled widow-lady, dressed in black, with her knitting in her lap. Now, she's more likely to have had cosmetic surgery, to be dressed fashionably and out and about, cruising, scuba- and sky-diving with her equally-active husband!
Given that they're both doing today much the same as their grandchildren in their thirties are, the idea of being 'old' just doesn't register with them. Very few people, short of perhaps their nineties, will ever claim to be so many years "young."