I favour making contact - but NOT telling them that they're wrong (cos it might be that they're not ... and I am!)
My usual message tends to run something like "Hi - I see from your tree on [site] that we're both interested in Nebuchadnezzar Ashbie [or whoever], who was my great x11 grandfather. Most of our research appears to tally, but there are a few places where we have arrived at different conclusions, in particular:
[list of discrepancies]
Would you be interested in exchanging notes on the evidence we have each relied upon, to see if we can get to the bottom of these differences?
Kind regards ..."
I've been ignored more often than not ... but I've never been accused of being rude or unhelpful (yet ...)
I have, however, encountered the "stolen ancestor" phenomenon referred to by the OP. A certain, extensive family tree has appropriated my great uncle Ken, married him off to one of their womefolk, and given him children and (I think) grandchildren.
Same name ... wrong man. My great uncle Ken was a homosexual who moved to America to gain greater acceptance. He never married, never fathered any children, and died in 2002. My great aunt Shirley (who is still alive) scattered his ahes in the potomac. He does NOT belong in this other family tree ... and nor do any of his forebears, all of whom are also my forebears.
I have written and told him this, but to no effect.
And, you know, I feel strangely violated by this. Not, so much, by the fact that they have miappropriated by forebears (whom I share with LOADS of other people ... my grandfather and great uncle Ken had 8 other siblings besides Shirley; their father had seven siblings; his father had 9 siblings; his father had 7 siblings ... yep: there's plenty of other people who share my forebears!) but by the fact that they are wrongly accusing my great uncle Ken of having been a married heterosexual with children. It took a lot of courage in the 1940s and 1950s to be open about one's homosexuality; and somehow their claims that Great Uncle Ken was married with children seem to detract from the courage he showed. That doesn't seem fair to him at all![/list]