`ls` shows file, `bash` says "No such file" ???

[Tom Roche <Tom_Roche@pobox.com>]

For background on my problem (and why I very much need to solve it), see http://forums.linuxmint.com/viewtopic.php?f=190&t=166506&p=855700#p855700

But the essence of the problem appears to be

me@it ~ $ /usr/local/share/firefox-3.6.28/firefox-bin
bash: /usr/local/share/firefox-3.6.28/firefox-bin: No such file or directory
[127]me@it ~ $ lsalh /usr/local/share/firefox-3.6.28/firefox-bin
-rwxr-xr-x 1 root staff 44K Mar  6  2012 /usr/local/share/firefox-3.6.28/firefox-bin
me@it ~ $ sudo /usr/local/share/firefox-3.6.28/firefox-bin
sudo: unable to execute /usr/local/share/firefox-3.6.28/firefox-bin: No such file or directory
me@it ~ $ groups
me sudo staff lpadmin

How is it possible that `ls` can list a file, but `bash` says "No such file"?

Note that everything else seems to work on this box, which FWIW is

me@it ~ $ uname -a
Linux it 3.11-2-amd64 #1 SMP Debian 3.11.8-1 (2013-11-13) x86_64 GNU/Linux
me@it ~ $ cat /etc/debian_version 
jessie/sid

so it's not like the box is "just broken." FWIW, /usr/local/share/firefox-3.6.28/firefox-bin is 32-bit, while the rest of the box is 64-bit. I don't see how that could cause *this* problem, but that's the only thing unusual about /usr/local/share/firefox-3.6.28/firefox-bin (of which I'm aware).

desperately confused, Tom Roche <Tom_Roche@pobox.com>