A batter hits home run but doesn't touch home for some reason. This happened a few years ago with Robin Ventura in a playoff game. The winning run had already scored on his home run, but he was mobbed by Todd Pratt (runner on first at time of hit) and didn't continue to second. Since it was virtually impossible (and unnecessary) to continue he stopped at first, that play is considered a single, even though he hit it out of the park and is widely considered as "The Grand-Slam Single"
If a batter hits a home run in the first inning, and the game is wiped out due to rain before the fifth inning: If the game isn't official, none of the stats count, not even towards career totals.
A simpler answer is that because player's stats are based on calculating total from game stats. If the run didnt count in the game it wouldn't show up in the game stats, hence, it wouldn't show up in career stats