When you say you deleted duplicate files from Media Player I dont think that is correct.
Media Player was listing the same files that were in iTunes so when you deleted the ones in Media Player you were also deleting the ones in iTunes.
Note that music files are not actually "IN" media player or iTunes, all those applications are doing is listing files that are on your hard disk.
The reason the file still played in ITunes when it was in the recylce bin was that iTunes probably updated its database to point to the file in the recycle bin.