Do Readers Really Become the Viewpoint Character?

Every so often I come across a piece of writing advice, or rule, or opinion that leaves me perplexed.  Here's one I've been seeing a lot lately.

Readers become the POV characters in the stories they read.

What? Really?

Here's an excerpt from Deep Point of View, by Marcy Kennedy.

As readers, we're not simply experiencing the story along with the viewpoint character. We become the viewpoint character. We climb inside their mind and body.

I don't know about you, but that's not the way it works for me. I may feel that I'm in the same room as them; I may even be peeking around inside their heads, but I'm definitely not them. Not even close.

I've often wondered if the people who say this don't quite mean what they appear to be saying. Perhaps they really mean "We ride along with the viewpoint character.", But I've seen this sentiment voiced so often I think they really mean it. So are they wrong, or am I simply different from everyone else?

I don't mean to imply that I sit back and watch the scene at a distance, like I'm at a movie, although that can be the case when the POV is distant enough.  But no matter how deep the POV, no matter how much I'm inside their head, I'm still a separate observer. I may be sitting in the same roller coaster as the viewpoint character, experiencing the same sorts of thrills, but there's no overlap between the two of us.

To be honest, I don't understand how anyone could feel as though they were the viewpoint character.  He/She constantly makes choices or says things that I would never consider doing, so I'd never be able to maintain the illusion of being them. Heck, authors typically go out of their way to have characters do the exact opposite of what we readers expect them to do. For example, when the POV character sees the magic ring that will allow them to vanquish the bad guy, and  we're yelling at them to pick the damn thing up and fulfill their destiny, but the character says "no way" and does their best to ignore the ring. Or how about when readers scream at a character because he's not asking the girl to dance even though the girl is so obviously smitten with him that my cat rolls his eyes at the character's stupidity. Are we screaming at ourselves?  I think not.

So is it just me, or do the rest of you become the viewpoint character when you read?

Thanks.

ChemistKen