To me, colors are important. I'm a visual artist. The minimal amount of colors to me is an additional two to your two. It's not arbitrary, I didn't just go crazy with colors, I settled on exactly four because I couldn't reduce it to three.
This is a fundamental misunderstanding of what minimalistic design means.
If you've identified that you need a website, minimalism would be paring that down to the core essentials and ensuring it has everything it needs, but nothing more, to suit its purpose.
Websites exist to serve content. The author of this page demanded it have a background image.
Here's another page that doesn't:
That's a design element that serves the functionality well and doesn't feel superfluous at all. But the image on the colophon page I'm less excited about. It gets in the way and feels unnecessary.