If they both solo, and both start at the same time they have the same score. Working as intended. We have 8-12 guys with that score every pit raid. It's RNG who will get the first and second place rewards in the case you presented.
If both people start the raid and x damage has been done, then they solo. Both will end up with total - x damage. There is nothing crazy going on there.
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No, only damage corresponding to the health the enemy had counts in your total.