I figured it out. Muse is stripping the colour profiles from images. Viewing on a wide gamut monitor, we need an sRGB tag otherwise the colours are over saturated.
Test it yourself. On your wide gamut monitor. This effect will not be present on laptop displays or even most imacs.
Insert an sRGB tagged image into muse. Preview that page in browser, right click and download the image. Open the downloaded image up however you please and check for the colour profile; it's gone.
Adobe, please fix this. You're dealing with professionals who need proper colour management. I don't want someone on a wide gamut monitor to view my site and get the impression I can't control saturation when grading images.
THIS IS AN EXTREMELY EASY ISSUE TO FIX.
Wordpress has the same problem. To fix it on Wordpress one replaces the default image processing engine with ImageMagick. The ImageMagick engine is open source so theoretically you guys could patch it in if you wanted; or just disable or give an option to disable colour profile stripping.