MacOS – MacBook Pro updated to EL Captain 10.11 but QuickTime Player didn’t upgrade

How about this: It's not exactly what you want, but achieves roughly the same thing.

I seem to remember pre-OS X you could activate an app and keep it from being frontmost, but that appears not to be possible these days (or I imagined it.)

to replaceFrontQTPlayerWithFile(aFile)

tell application "QuickTime Player"
    activate

    try
        set frontDoc to front document
        close front document
    on error err number errNum
        if errNum is -1719 then
            -- There is no open document
        else if errNum is -10000 then
            -- Front doc exists, but does not really...
        else
            log err
        end if
    end try

    open aFile
    play front document

    -- Hide QTP
    tell application "System Events"
        keystroke "h" using command down
    end tell

end tell
end replaceFrontQTPlayerWithFile


on run
    set unixFile to "/Users/diggory/Music/iTunes/iTunes Music/Music/Underworld/Oblivion With Bells/01 Crocodile.m4a"
    set macFile to POSIX file unixFile
    set fileRef to (macFile as alias)
    my replaceFrontQTPlayerWithFile(fileRef)
end run

I know you "don't want to reinstall OS X," but the easiest way to reinstall Quicktime (the current version, which is not a standalone download) is to reinstall Mountain Lion via Recovery Mode. Following the introduction of Lion, Quicktime became apart of the OS X installation package. There is no need to take a roundabout method. Reinstallation using recovery is non-destructive and only reinstalls OS X builtin applications and system components.