Shoot flat and or capture color with camera?

Just beginning to use my DLSR to shoot wildlife footage.  Regarding Picture Style and color correcting, I've seen tutorials that recommend shooting flat (like exposing to the right when shooting stills) and do the magic in post-processing. I've also seen tutorials that recommend capturing as much color as you can during the shoot so you have little or no post-processing to do.  What were you taught or what works best for you when shooting outdoors and want a natural look.  I'll be shooting with a canon 7D mark II.

Arguably, shooting flat and color correction/grading in post *can* and frequently does produce a more pleasing image that is closer to how the eye sees the scene. Shooting flat and post correction can reveal shadow detail that would be difficult in a conventional workflow.

But it does come back to one's skill in using those post tools... As well as shooting skills. The lessons (eye training) learned in processing raw still images certainly apply, though most of the video tools are different.

I like to make a differentiation between Videography and Cinematography (aka. "filmic" shooting) - there are different values in these two disciplines.

In Videography we understand that we don't control the set, we will have one chance to capture the content, and we need solid shooting skills that reflect that. We'll typically do little in post correction/grading.

In Cinematography we control the set, we get re-dos until we run out of light, money, food or good-will, and post correction/grading is an expected part of the workflow.

The conventional advice is to learn Videography first, then, build your Cinematography practice on that solid foundation. For what it's worth...

There is a difference between expose-to-the-right and shooting flat... but nothing screams "video" like blown highlights.

PS. When shooters talk about shooting flat, they usually mean much flatter than is available in Canon's profiles, they mean custom profiles.