Trash It is an AppleScript app, and as such, it almost certainly uses code very similar to one solution that was posted, involving a Unix command. If that particular solution didn't work, nothing would.
(1) Error -8003 is not documented by Apple (and it's "-8003", not "8003"). The number suggests Carbon (which is supposed -- but only supposed -- to be gone from SL), that is, a Finder error. But, even if it were documented, it might not tell us much. It could say something like, "Cannot delete file or folder", which would leave us pretty much where we are. It seems likely that there is more than one possible cause for this issue. If so, that could explain why not all methods work in all circumstances.
(2) Applications mentioned in this thread (such as TrashIt, Onyx, Cocktail) work by means of AppleScripts calling tools built into the system, with the authorisation granted by the user. IOW, they do exactly what a knowledgeable user can do from Terminal; the stress being on knowledgeable.
The expert user likes to be in control and to know exactly what is being done, so clearly these apps are not for him. But the less knowledgeable user runs the risk of doing serious damage with just a small typo, so using these apps is probably safer than dabbling in Terminal. So, if you just want to be productive without worrying or learning about what's under the hood, by all means use TrashIt, or Onyx, or whichever one works for you -- and do pay the shareware fee or make a donation; after all, they saved you time and money.
But, if you are willing to spend some time and effort learning how to do stuff for yourself, try CLIX.