The reason is simple: the tonearm's ability to properly track the cartridge far outweighs what cartridge you have. The better the arm is at this, the less differences you'll hear between cartridges assuming they are set up properly.
So absolutely true! Not only does a great tonearm allow for proper tracking, but a great tonearm has a sound of its own due to how it handles vibrations from the cartridge. There is not a tonearm on Earth that neutralizes all stylus induced vibration. Perhaps only 5-10% of the overall sound quality comes from the material and design choices but they still count. When I switched to Reed 3P tonearms the SQ change was revelatory.
After the choice of tonearm, invest in the phono stage before cartridge. There are so many great sounding sub-$1500 cartridges. And as noted above, cartridges are subject to wear and to accidental damage.