It IS supposed to match.

                        q/"this"string"/ =~
m{
    "                   # X
    (
        [^"]*?          #  XXXX
    )
    "                   #      X
}x
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Remember why "foo" =~ /o/? It's because there has to be an o in there, but it's location in the string has not been fixed in the regex. Anchoring avoids this problem. ^ matches the null string at the beginning of a line or string, $ matches the null string at the end of a line (right before \n) or string.

"foo" !~ /^o$/;

q/"this"string"/ !~ /^"([^"]*?)"$/;
#                    X          X
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++ vs lbh qrpbqrq guvf hfvat n ge va Crey :)
Nabgure bar vs lbh qvq fb jvgubhg ernqvat n znahny svefg.
-- vs lbh hfrq OFQ pnrfne ;)
    - Whreq