You are right, my change did not affect greediness. The bad thing is: now I don't understand why my proposed solution worked at all. Maybe someone can explain? I don't think the question is too important, but I like to use regular expressions and it bugs me a little if I cannot understand one (especially such a tiny one).
I have read the documentation you have cited and it helped, so I played around some more and tried out the following, which only exchanges "+" for "*" in your original expression, really works as one would think and therefore would be my preferred solution, at least for Perl 5.10:
$_ = "Hello";
print "$1\n" while /(?=(.+))/g;