They both do.
http://www.sportsnet.ca/hockey/nhl/oilers-split-puck-marincin-miller-milestones/
That example is probably more common than yours - rookies sharing first point and first goal.
As far as the original question...I think it's basically a moot point. One gets a goal, the other gets an assist. Of the 200 or so goals a team gets per year, there HAS to be at least 1 or 2 whose scoring is questionable. I think that small amount of error built into the system is okay. Other than the handful of players trying to reach contract bonuses, or going for the individual awards, or trying to break a record that couldn't otherwise be broken, I don't think the players really care at all. And you can make the argument that if you needed that goal to make a contract bonus, maybe you should have worked harder to get one more goal elsewhere. (AFAIK, most of the bonuses I'm familiar with are more as insurance that you only have to pay a player if he produces some reasonable results and doesn't wind up on the bench due to injury. But I could be wrong.)