I hate this advice. It's not "wrong," in the sense that technically it would be a good thing to do, but it's also so wrong that it transcends categories of right and wrong.
Your refill schedule will not allow you to get extra prescription meds early. And if it did, your insurance wouldn't pay for it - which means paying sticker price, which means ... well, depends on the med, right? I used to take an antacid that had a sticker price of about 800/mo.
For almost anyone, "stock up on an extra month of prescription meds" isn't a thing. It's just not a choice. For it to /be/ a thing, someone actually needs to write a law stating something like "once per calendar year, a physician can write an extra parallel prescription for a supply of medications not exceeding three months, and insurers must pay for it," or somesuch.
Until that happens, I don't even know what to /do/ with that kind of "advice."