The where clause is exactly the same as before. The only difference is that we are now (deliberately) setting the partitioning column equal to itself. This will not change the value stored in that column, but it does affect the outcome. The update now succeeds (albeit with a more complex execution plan):
The optimizer has introduced new Split, Sort, and Collapse operators, and added the machinery necessary to maintain each potentially-affected nonclustered index separately (using a wide, or per-index strategy).
Read on for the reason why this happens, as well as a few solutions.