I know this sounds anal, but if they were to simply clean up the site a bit like by removing all the excessive icons and cleaning up their button text, they would come across as more credible.
Perhaps if they came across as more credible, people wouldn't be leaving and google wouldn't get the wrong signals.
Simple and quick list of changes that would make their site feel more trustworthy:
1. Remove most if not all of the icons 2. Do away with borders on non-white background - basically just make background white. 3. Tone down your button text. "I'm ready to learn" sounds really shitty and obnoxious. 4. Stop screaming with all caps buttons 5. Consider a different logo entirely. 6. Consider different color palette entirely 7. Do away with old button styles 8. Restore normal font size to sources - right now it makes me feel like you are hiding them. 9. List author credentials on every content page 10. Do away with ugly callout styles and excessive icon usage 11. Re-work all the weird "Scientific Research on ___" tabs so that they do not require so much clicking to find basic info.
Overall, the site is just over-designed. I realize everything I say would make the site look more WebMD-like, but that's what triggers trust when it comes to medical info sites.
Lastly, I fully expect to be downvoted for this as design is not something that's very respected around these corners of the web, but I felt it was important to make that point since this is a perfect example of a website that while looks great, does the opposite of creating a trustworthy browsing experience.