While I can't speak for Piggies&buns I strongly agree with their statement and heres why:
Parasite resistance has been seen in cats and dogs because of routine prevention treatment giving rise to the 'super flea', something you normally hear about it every few years. For example any vet practices who used the likes of Frontline for fleas (active ingredient: fiprinol) had to change to a different medicine like Advantage (active ingredient: imidacloprid) or Advocate (active ingredients: imidacloprid and moxidectin).
As Siikibam mentioned, parasites can become resistant much like we can with prolonged and unnecessary antibiotic use. Eventually the bug/parasite will become immune and a different or stronger medicine will be needed.
It's worth noting that fleas, in general, are host specific (excluding cat fleas. They'll munch on anyone). For example your cat isn't going to get fleas from a hedgehog. Neither is you guinea pig going to get them from a dog. My point is, for your pig to have fleas, it's got them from another animal as they aren't a natural host for them.
Lice typically comes off the hay and is easily treated by the vets. Mites you can't see, and will need a diagnosis from the vets and they'll prescribe the appropriate treatment. Typically these are seen more often than fleas but regardless, it takes more than one dose to eradicate them. You also need to keep on top of the cage hygiene as these bugs will live in the environment too.
The last point I want to make is, like Eriathwen mentioned, dosage. Members of the public aren't expected to know how to calculate the correct dosage for their pet. Over the counter medication is a lot weaker than prescription drugs to lessen the risk of overdose. This unfortunately means that over the counter antiparasite treatment isn't effective and just suppresses the symptoms, if anything at all.
Overdose of ivermectin seems to be more and more common now; I hear about it all the time. I've heard of quite a few deaths due to ivermectin overdose in Guinea pigs, especially during the pandemic. While done with good intentions, ivermectin can and does kill. Those lucky enough to survive typically suffer with neurological problems as a result.
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@Womble; please know that not all scratching is caused by parasites. More importantly, I'd have your new piggies checked over by a vet and quarantined for a minimum of 2 weeks before meeting your other pigs. This will help prevent any disease spreading through the herd which I'd be more concerned about than them scratching. The vet will also be able to rule in/out the possibility of parasitic infection and advise you on the best course of action.
Here's a list of our recommended piggy vets:
Recommended Guinea Pig Vets