It was just a reference to the person in the story, not an allusion to "because he was old he didn't try to update his knowledge/continue learning".
If your answer is that 'it's just part of the story'. Well that's precisely the complaint.
It simply means someone experienced/being at something for a long time. The greybeards at a company can be all women of the age 26, but if they been with the company for 5 years when the company got started 5 years ago, they are the greybeards of that company.
Might as well say "veteran" or "old-timer", although "old-timer" would imply actual old age, "veteran" implies nothing like that.
Greybeards is an inclusive term and it's a well known term.