Various sources list Hillsdale winning by 14-12
Other sources list the game tied at 10-10
Note from Gary Kusch: I found an on-line game article in a publication called "The Notre Dame Scholastic" dated 11/26/1892 which gives almost a play by play description of the game for each half. The first half summary says the game started at 2:30 and Hillsdale went ahead 6-0 by scoring a touchdown (4) and goal after (2). Notre Dame later scored a touchdown, but failed on the goal after. Thus, the first half summary ended as follows: Score 4 to 6 in favor of Hillsdale, Time 1/2 hour. The second half started at 3:25. Hillsdale scored at the 6 minute mark, but failed on the goal attempt for a 10-4 lead. Notre Dame scored on their next possession and made the goal to tie the game at 10-10. The game sort of went back and forth from that point. Hillsdale moved within 10 yards of Notre Dame's goal but fumbled. Notre Dame punted and then recovered another Hillsdale fumble. Notre Dame was driving when time was called "on account of Hillsdale having to take a team." The summary statement of the second half was: Score: 6 to 4 in favor of Notre Dame, Time 1 hour.
I found nothing in the article suggestive of any controversy, although I am not sure what is really meant by the quote above "on account of Hillsdale having to take a team." It sounds like they had to catch a train back or something. Prior to the first half summary, the article was very complimentary of the Hillsdale team saying that the work of the team was faultless, and that their only desire was they wished to play a return game, which the article agreed should be accorded them. It continued that for nearly two hours the teams struggled to gain each other's goal, but only twice did each succeed. It ended by saying that their was disappointment when time was called at 4:30 with the score standing at 10-10.