They can use the terminology all they want; the people you point to are not above political pandering for more funding to buy cool toys.
The great thing about adding the word 'near' to 'peer' is that you don't have to define exactly how near they are. There are more than a few tactical publications, signed by Admirals, that don't consider these nations' assets to be 'peer' or 'near peer.'
We want a world where we can impose our political, military, and economic will uncontested. We had a good 20 year run where that pretty much happened, and now China and Russia are able to exert more influence in their geographic regions. That doesn't make them peers, it just means they're more than what they were. But we'll call them peers and make it sound like they're fixing to invade us any minute if it means it approves the next [insert major military program that needs funding].
The bottom line is that saying someone is a peer doesn't make it true. We're now playing the same game we played in the 60s-80s with the Cold War -- the USSR was a 'near peer,' until 1991 when we all found out it wasn't even close.
Nice cliches. You really think that China or Russia is capable of launching a mainland invasion of the U.S. at any moment now?
I don't think I'm underestimating anything. I acknowledge that China has built a relatively formidable brown water Navy. Unfortunately, China's 'brown water' contains the most traveled shipping lanes in the world and that conflicts with our economic interests, and that sucks. But the fact remains that they're a brown water Navy.
I'm also not underestimating that setting up a base of operations near China in any future conflict would be nearly impossible, simply because of geographic constraints. But that has a lot more to do with the shape of the Earth than it does with the state of China's military.
However, I wouldn't go so far to call China a peer. They have enough of a military and production to make armed conflict with them on their own territory somewhere between undesirable and hard to win, but they don't have the ability to exert their influence globally. When China starts conducting routine ISR missions in the Gulf of California with a CSG sitting 50 miles from LA while Russia routinely deploys multiple SSNs/SSGNs to the Gulf of Mexico and has a Carrier sitting 50 miles off of DC, I'll start worrying about these countries being 'near peer.'