Looks like this bug has been around for quite a while! Here are some bug references you may find helpful (and may want to subscribe to / vote up, hint, hint...):
Debian bug #85123 ("sudo: SECURE_PATH still can't be overridden") (from 2001!)
It seems that Bug#20996 is still present in this version of sudo.  The
  changelog says that it can be overridden at runtime but I haven't yet
  discovered how.
They mention putting something like this in your sudoers file:
Defaults secure_path="/bin:/usr/bin:/usr/local/bin"
but when I do that in Ubuntu 8.10 at least, it gives me this error:
visudo: unknown defaults entry `secure_path' referenced near line 10
Ubuntu bug #50797 ("sudo built with --with-secure-path is problematic")
Worse still, as far as I can tell, it
  is impossible to respecify secure_path
  in the sudoers file. So if, for
  example, you want to offer your users
  easy access to something under /opt,
  you must recompile sudo.
Yes. There needs to be a way to
  override this "feature" without having
  to recompile. Nothing worse then
  security bigots telling you what's
  best for your environment and then not
  giving you a way to turn it off.
This is really annoying. It might be
  wise to keep current behavior by
  default for security reasons, but
  there should be a way of overriding it
  other than recompiling from source
  code! Many people ARE in need of PATH
  inheritance. I wonder why no
  maintainers look into it, which seems
  easy to come up with an acceptable
  solution.
I worked around it like this:
mv /usr/bin/sudo /usr/bin/sudo.orig
then create a file /usr/bin/sudo containing the following:
#!/bin/bash
/usr/bin/sudo.orig env PATH=$PATH "$@"
then your regular sudo works just like the non secure-path sudo
Ubuntu bug #192651 ("sudo path is always reset")
Given that a duplicate of this bug was
  originally filed in July 2006, I'm not
  clear how long an ineffectual env_keep
  has been in operation. Whatever the
  merits of forcing users to employ
  tricks such as that listed above,
  surely the man pages for sudo and
  sudoers should reflect the fact that
  options to modify the PATH are
  effectively redundant.
Modifying documentation to reflect
  actual execution is non destabilising
  and very helpful.
Ubuntu bug #226595 ("impossible to retain/specify PATH")
I need to be able to run sudo with
  additional non-std binary folders in
  the PATH. Having already added my
  requirements to /etc/environment I was
  surprised when I got errors about
  missing commands when running them
  under sudo.....
I tried the following to fix this
  without sucess: 
- Using the "- sudo -E" option - did not work. My existing PATH was still reset by sudo
 
- Changing "- Defaults env_reset" to "- Defaults !env_reset" in /etc/sudoers -- also did not work (even when combined with sudo -E)
 
- Uncommenting - env_reset(e.g. "- #Defaults env_reset") in /etc/sudoers -- also did not work.
 
- Adding '- Defaults env_keep += "PATH"' to /etc/sudoers -- also did not work.
 
Clearly - despite the man
  documentation - sudo is completely
  hardcoded regarding PATH and does not
  allow any flexibility regarding
  retaining the users PATH. Very
  annoying as I can't run non-default
  software under root permissions using
  sudo.