Run the search again if need be, but look at the source of the info. If it's from an ancestral file or pedigree resource file, then it was posted by a family researcher, probably Mormon, probably related to his adoptive parents in some way. The 'ancestral files' can be loaded with errors. The 'pedigree resource files' can too, but they were submitted more recently and tend to be a bit better. There is a small fee for receiving the full file on CD but if it's the best lead that you have, it may be worth it.
If it's only in the Social Security Death Index, then you should order a copy of your father's original application for his SSN (use this search engine -- it has an automatic request form generator--
http://ssdi.rootsweb.com/ ). That will allow you to confirm both his parent's names and may provide you with other valuable hints. Same for his adoptive father if he's in the SSDI.
I would advise against signing up for ancestry yet -- you don't know enough to make it worth the money.
Use these free bbs to see if anyone else is looking for the same people:
http://boards.ancestry.com/http://genforum.genealogy.com/