I've heard that said a number of times over the years, but I've never honestly understood why. Not that I know better, it just goes against my personal feelings.
Mains or sub would be my guess as to the most important speaker, followed by the center. If only because you can run a phantom center with good results, but have you ever tried running without mains? Subs should be self explanatory as good bass is a godsend and can add significant value to a system.
You can watch the TV without external speakers or other components. The others just add to the quality of the experience. If you want the minimum a center channel is not necessary. Neither is the sub as the mains can produce bass. After the necessities are in place you begin improvements. You add a high quality sub and bass is improved over just the mains. Adding a center can sound better than just the mains. A mediocre center may not be much of an enhancement (especially in the dialog). The better the center the more enhancement. Saying that the center channel is the most important speaker does not mean that it should be the only front speaker. It means it should be the best of the three fronts.
Personally I would rather have a great center and decent mains as the other way around for watching movies. The most annoying thing is having to constantly adjust center volume up and down or rewind to hear dialog that you missed due to a crappy center speaker.