You never completely "eliminate" anyone, because 9 times out of 10 as an investigator you have already interviewed the one responsible even if only briefly.
More than likely they have evidence to support their theory of a stranger abduction, which is bolstered by the FBI's contribution (profile etc) ..
In EVERY case you'll get a million theories, some will have merit , some will be out there like Pluto. Some will swear its the butler, some swear it's the Zodiac (again). What you have to do is follow evidence
The thing to remember is that all people can go on is whats released, and in some cases, wrong info is deliberately released, or more often withheld .
Those with no investigative experience, can only base things on what they are familiar with , given such info, so theories will abound.
However LE isnt bringing in the Feds, to create a profile of an offender , only to release it to the public, with a chance that this offender just may kill again, IF they feel it had something to do the parents of one of the victims.