Source is here, starting on page 53, there's a nice table of life expectancy by age and date: https://www.cdc.gov/nchs/data/nvsr/nvsr65/nvsr65_08.pdf
I'd argue this has an impact on the "savings rate" per employee, but not on the average payout length.
Your argument is only correct if we define the average payout length to only factor in those employees who receive at least one check. However the original quote that you claimed was wrong is referring how much the pension has to pay out on average, which is not limited to those who live long enough to collect a payout. Their average payout length of 3 years factors in a whole bunch of $0 payouts, whereas your average ignores all of the zeros.
And that's a very hard number to come by, because as I've argued you would have to factor in all other reasons why a pension might have to be paid out longer or not at all.
Certainly "3 years of average payout" must be completely and utterly wrong because this number includes infants etc which were never employed. Infant and child mortality has an enormous impact on average life expectancy.