If there is oil under the starter, especially on an 05, there is a very good chance that you do have a bad seal on the starter that will allow some oil from the primary to seep into winding of starter and eventually lead to a short.
As Gas and TJ, indicated, BDM did replace many of the suspect starters back then including mine. Always heard it was a seal problem with some of the starter they got from their suppliers and not sure of all the detail, but it may be just as simple as getting the right gasket or o-ring and replacing it.
Be careful though for if it is leakage going past that seal, it will get into the winding and short sooner or later. If you can fix it before then, good electrical cleaner that leaves no residue (make sure they shit is safe for plastic so not to remove the shelac and insulation coating off), will hellp clean any oil build up and should get you going.
Good luck and let us know how you make out.