Relationship Finder's results are only as good as the genealogy on which the results are based. If your genealogy and these others' genealogies are valid, then your results are valid.
If you are not related to John Adams but you are related to John Quincy Adams, that probably means you are related to JQA on his mother's side. Relationship Finder will show you the shared ancestors and lineages it found.
Some members list these relationships in the biography sections of their profiles. You can also put them in a free-space page, and link to it from your profile.