I grew up in bear, mountain lion, wolf country, and I can see both points of view. SOP for a mountain lion is stand up tall, open your jacket or shirt (to make yourself look bigger) but do not yell, speak calmly. Throw rocks and fight back if necessary. This mostly works. The main incidents of mountain lion attacks are in places where their habitat buts up against a dense human area where they get lazy and stalk trail runners, bikers, etc.

A grizzly though. Make yourself look big... and don't run... but everything else is pretty much what to do once you are already on the ground getting chomped.

Black bears are fucking pussies most of the time.

That said, it's important to distinguish between the type of encounter, between a surprise and stalking. Stalking (repeated sightings, etc) means the animal is already considering you as prey.

You are right that if a big cat comes for you, you won't see it coming until the last few seconds (read up on non-dog big cat hunts...) but honestly a big cat is normally just warning you off it's territory. A grizzly is much more likely to decide you look like a threat that needs dealing with or eating...

So I agree with Rabinowitz in general.

Story time, I recently was going up a canyon in a very remote area and came across a track in the creek bed that froze me in place... because at a glance I thought it was a mountain lion (remote canyons are a favorite for their dens). My heart raced until further inspection indicated it was a black bear track and was at least 2-3 days old... and I breathed a sigh of relief. (sometimes its hard to tell what made traks, other times not)

Here, I found the pic I took for those curious.

https://commons.wikimedia.org/wiki/File:BlackBearTracks.jpeg