I can't imagine anyone sugesting that mower blades should be tossed when they get dull any more than you should toss a knife when it's dull. I think he may have been joking (as I have joked that if the dishes are dirty, then it's time to throw them away)
However, if there's a sale on blades, it's nice to have two sets, one set that's sharp and hanging on the wall and the other set that's on the machine. This technique makes it easier to decide that it's time for the sharp blades and you can do a quick switch. It also means that if you hit a rock and chip or bend a blade, you can fix it quickly and finish the job.
Cliff