His point is still fair though - older cells don't perform as well.
How old is "older?" Would that happen in a single batch of beer, or are you talking about repitching?
This is a more complicated question than it may seem
There are two ways that scientists talk about how old a yeast cell is - replicative lifespan, and chronological lifespan. Neither of these is investigating the health of cells that are fermenting without dividing over time so the results may not be directly applicable. With that caveat . . .
The replicative lifespan of yeast is roughly 25, meaning it can divide 25 times before it stops. I am making a broad generalization here because it is strain specific. This number comes from my old labs' work on strains BY4741 and BY4742, common lab strains that are the opposite mating types but otherwise the same. I never did lifespans on any brewing strains because it is a huge pain and requires a dissecting microscope - basically, you plate cells, use the dissector to move individual cells to their own spot on the plate, then incubate for 2-4 hours. Then you go back to the scope and pull the daughter cell away from the mother, put it in a garbage area, and count that as one. You do this again and again until the mother stops dividing. You can't let it grow too long or it can become hard to tell the mother from the daughter, or you may count the daughter's daughter as a daughter of the mother. It is very labor intensive - we had a group of people who did nothing but pick daughters all day long because they went through the entire yeast deletion collection, ~5000 strains that are the same as above but with a single gene deleted, plus controls, etc.
Anyway, older mothers don't perform as well as younger mothers. Daughters of older mothers don't perform as well as daughters of younger mothers, although they recover after a couple of generations. I believe in this case "perform" means grow, they were not checking for fermentation performance or anything like that.
The other kind of aging, chronological aging, is quite a bit different. In this case, a strain is grown to stationary phase and let sit for some period of time and then tested to see if it will grow again. Again, the entire yeast deletion collection was screened by a guy I know (much easier for one person to do). The normal strain was 50% viable at ~2 weeks. This is misleading though, because the media used affected the results. Another guy I know showed later that the effect was almost entirely due to pH, and more specifically the ability of the strain to withstand acetic acid.
So, will this happen in a single batch of beer? The scales for a single fermentation are too short to apply to either one of these sets of data. If you are constantly repitching replicatively older cells I think you will notice in your fermentations. But isolating replicatively older cells is a real pain, labs have spent years trying to figure out how to enrich a culture for older mothers. If you are harvesting from a carboy don't worry about it. From a conical, as long as you are blowing out the first bit to get rid of the trub, don't worry about it.
If you are constantly over pitching and re-pitching from an over pitched batch, you may be increasing the chronological lifespan of the culture. However, the data there are not good enough to give a definitive answer. We know there are pH effects, but the final pH of the research media is not in the same range as beer, the finished culture ends up much lower than beer (under 3) while the buffered cultures they used are higher than beer (pH = 6). And they didn't do anything with serial repitching of these cultures.
I think I typed all of this stuff and didn't answer the question. Bottom line - if you follow standard practices you should be fine. Make starters, aerate well, pitch in the suggested range, etc. If a culture gets old by sitting for a while, refresh it in a starter. Don't worry about bud scars.