This is all helpful but I'm leaving this marked "need info" until someone has the time to do a broader investigation of what we get in $0 and $_ for invocations of a trivial script with many different shells.  Note that there may be up to three different shells involved: the shell you're typing commands at, the shell invoked by 'sh', and the shell named on the #! line.

No problem. If I create,

$ cat configure
#!/bin/sh
echo $0

in my home directory, then at least in bash and dash, the $PATH entry gets prepended to $0 when it is needed to resolve "configure":

$ PATH=/home/mjo configure
/home/mjo/configure
$ PATH=. configure
./configure

Having tested on one platform and two shells, I conclude that there's no way to get "configure" without a directory separator, unless "sh configure" was used :)

Alas, someone wrote that $as_myself code for a reason, so we're probably not so lucky. I see the problem and if it's not fixable, that's OK. IIRC we only wound up in this situation because someone created a tarball with a non-executable configure script, and then the person writing the workaround was unlucky and left out the "./". And then I was even more unlucky and had both a shell without LINENO, and some other "configure" in my $PATH. It's not worth spending a lot of time on.

(This is copy/pasted in its entirety from an old bug- mailing list post of mine)

In the configure scripts that I'm generating, I see the following
variable assignment:

  # Find who we are.  Look in the path if we contain no directory
  # separator.
  as_myself=...

Later, this may be used to re-exec the configure script with a better shell,

  exec $CONFIG_SHELL $as_opts "$as_myself" ${1+"$@"}

But, consider the following scenario:

  * I have some other "configure" in my $PATH.
  * I have a shell that doesn't support LINENO.
  * I execute ./configure for some package by running "sh configure".

What happens in that case is that the "as_myself" computation fails to
find a directory separator in "configure", and instead searches my path
for a usable "configure". It finds one, but not the one I wanted to run!
Now I have

  as_myself=/path/to/some/other/configure/script

and then since my shell doesn't support LINENO, I wind up running

  $CONFIG_SHELL ... /path/to/some/other/configure/script

In other words, I re-exec the wrong script entirely. This can be worked
around by running "sh ./configure" instead of "sh configure", but leads
to a great deal of head-scratching.

Is this something that can (should?) be fixed?