Your comment appears to be what I needed to hear as changing the non-greedy match from /".*?"/ to /"[^"]*?"/ appears to work correctly. The negated character class was the trick.

I'm still a bit confused about why there is such a difference in what is matched, but I'm think about it some more.

Thanks for pointing me in the right direction.

I think you expect

perl -e'
    $_ = qq{...\n}
        .qq{<a href="foo">foo</a>\n}
        .qq{<a href="bar">bar</a>\n}
        .qq{...\n};
    s!(<a href=")(.*?)(">bar</a>)!$1\[$2]$3!s;
    print;
'
[download]

to output

...
<a href="foo">foo</a>
<a href="[bar]">bar</a>
...
[download]

but that's wrong. It outputs

...
<a href="[foo">foo</a>
<a href="bar]">bar</a>
...
[download]

The pattern says to match

• Match the start of the string,
  • followed by as few characters as possible (implicit leading /.*?/),
    • followed by the string '<a href="',
      • followed by as few characters as possible,
        • followed by the string '">bar</a>'.

Keeping in mind that "as few characters as possible" is zero characters, let's check if the string matches:

• Starting at the begining of the string,
  • Do 0 characters follow? Yes, so try to match the next atom.
    • Does the string '<a href="' follow? No, so backtrack.
  • Does 1 character follow? Yes, so try to match the next atom.
    • Does the string '<a href="' follow? No, so backtrack.
  • Do 2 characters follow? Yes, so try to match the next atom.
    • Does the string '<a href="' follow? No, so backtrack.
  • ...
  • Do 4 characters follow? Yes, so try to match the next atom.
    • Does the string '<a href="' follow? Yes, so try to match the next atom.
      • Do 0 characters follow? Yes, so try to match the next atom.
        • Does the string '">bar</a>' follow? No, so backtrack.
      • Does 1 character follow? Yes, so try to match the next atom.
        • Does the string '">bar</a>' follow? No, so backtrack.
      • Do 2 characters follow? Yes, so try to match the next atom.
        • Does the string '">bar</a>' follow? No, so backtrack.
      • ...
      • Do 25 characters follow? Yes, so try to match the next atom.
        • Does the string '">bar</a>' follow? Yes, so try to match the next atom.
          • We have a match!

• is there any difference between /".+?"/ and /".*?"/? Yes, + matches one or more of the previous pattern, and * matches zero or more of the previous pattern, but given that all strings seen in the table are more than one character in length, is there any difference since I am specifying that the pattern is non-greedy?
• is not the regular expression originally quoted non-greedy?
Thanks for any insight shared.

is not the regular expression originally quoted non-greedy?

It is. But what do you expect non-greedy to be? Some people think that non-greedy means "match an as short string as possible", without anything else. But there is just one such a string, and that's the empty string.

Non-greedy does not mean, "don't match where you would match otherwise". If a pattern matches with greedy (sub) matches, it will match with non-greedy sub matches. And if a pattern doesn't match with non-greedy sub matches, it will not match with greedy sub matches.

All greedy/non-greedy will do is change $&, it will not change whether or not a pattern matches.