Two solutions for puzzle KscuD

I'm new to Shogi, but this puzzle appears to have two solutions, though only one is accepted:
lishogi.org/training/KscuD
The accepted solution starts with 1. Rx31+, leading to a mate in 3. However 1. Rx31= also leads to a mate in 3, since gote is still forced to take the rook. Even stranger, when you turn on the engine in the initial position, it will say 1. Rx31+ is the only winning move (#3), but after 1. Rx31= (which it does not recommend from the initial position), the engine correctly says #2.

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