"close proximity"

In the US we often hear "close proximity". The media and other reports attempting to appear serious often use "close proximity". It appears to mean close or near. Questions: are the two words together a bit redundant? Is this just a US thing? Does one ever recall hearing "distant proximity" or "intermediate proximity"?

I believe "nearby" would be a better choice of words. From these Merriam Webster entries, it looks like you're right about redundancy:

Main Entry: prox·im·i·ty
Pronunciation: präk-'si-m&-tE
Function: noun
Etymology: Middle French proximité, from Latin proximitat-, proximitas, from proximus
Date: 15th century

the quality or state of being proximate : CLOSENESS

Main Entry: prox·i·mate
Pronunciation: 'präk-s&-m&t
Function: adjective
Etymology: Latin proximatus, past participle of proximare to approach, from proximus nearest, next, superlative of prope near -- more at APPROACH
Date: 1661
1 : immediately preceding or following (as in a chain of events, causes, or effects)
2 a : very near : CLOSE b : soon forthcoming : IMMINENT

"Usually the extra word is redundant, or such compound expressions can be replaced by single words, as shown in italics in the following examples:
in close proximity to ? near..." www.nrcan.gc.ca/ess/pubs/guide/gramm/jargon_e.html

Is the widespread use of the redundant word just a US thing?

It was used by a British playwright, librettist and liricist:
But then the prospect of a lot / Of dull M.P.'s in close proximity, / All thinking for themselves, is what / No man can face with equanimity. (W.S. Gilbert, _Iolanthe_, 1882)

_Webster's Dictionary of English Usage_ explains "Of course there are degrees of proximity, and _colse proximity_ simply emphasizes the closeness" and gives a few examples:

"in very close proximity" (Ken Druse, _N.Y. Times Mag._, 22 June 1980)
"in closer proximity" (Jane Nickerson, _N.Y. Times Mag._, 27 June 1954)
"in the closest proximity to" (Richard Jefferies, _The Open Air_, 1885)
"into close proximity" (Bell Telephone Laboratories, _The Formation of Ferromagnetic Domains_, 1959)

Redundant words are, sadly, pretty common in the UK. Some that spring immediately to mind are;
A free gift
A skin rash - you can't have a rash other than on your skin!
A dead body
I bet there are dozens of others!!

I must admit, it never occurred to me that there is nowhere else you can get a rash other than the skin, and actually is that correct? I'm not so sure.

But I gotta say that I have definitely seen live bodies - I've got one myself as a matter of fact. But there's no disputing there are many redundant words, and I'm sure they're universal.