True, this is the experiment they did in the original paper:
> Eighty-five older individuals [41M/44F, age = 68 ± 4 yr; body mass index (BMI) = 26.4 ± 3.7 kg/m2] had one leg randomly allocated to a single (1)-set and the contralateral leg allocated to four sets of unilateral knee-extension RT at 8-15 repetition maximum (RM) for 10-wk 2 days/wk. Pre- and postintervention, participants underwent magnetic resonance imaging (MRI) and unilateral knee-extension 1-RM strength testing.
Which, okay, it's old people who will get fatigued quickly and their recovery will be worse. Looks like some of them got tired and didn't recover well, while for others more sets were better because they recovered well, so when averaging those out this result is seems pretty believable, but I wouldn't generalize it to everyone.
My takeaway is if you get really exhausted/tired lifting, and you're doing 5 sets of 5 reps or 3 sets of 5 like you did when you were younger, maybe try 1 set of 5 instead, and you might find you recover better for the next lifting session. I personally have gone from 5 sets to 3 sets of my max weight a while ago because of exhaustion.