lol, whoever told you that has no understanding of how electricity works.That's why they both have to get replaced. I've "been told" that if only one bulb is replaced the current flow is unequal enough due the difference in the old v. new filament. The old bulb can't take the extra juice and fails. But by the time the new bulbs get to the point of failure, the old non-blown bulb's filament is about the same as the surviving "new" bulb. They won't last a whole long time, they're still old bulbs. But it gives enough time to get another two.
I also swap bulbs two at a time in all my vehicles, it's more force of habit since I put two fresh ones in, the idea that they would both die within a specified amount of time to one another sticks with me, since they're usually only rated to a certain number of hours based on coatings and filament material (for halogens) but I also do it with LEDs.
LEDs are different though, the only reason I would swap both is color temps - LEDs inch higher on the color temp scale over time, if you put a 50k hour rated LED that actually has 10k hours on it next to a brand new one, you would be able to pick out the old one by how much more blue it had become.