Problem with a shorter solution I'm looking at this problem.

[Title "White to move. Mate in three"]
[StartFlipped "0"]
[fen "5rb1/1p1P1pbr/1p5p/5N/PP2k/1Np3QB/6K/8 b - - 0 1"]


It requires white to mate in three. The accepted solution starts with 1. Kf1. But there seems to be a mate in 2 via 1. Ne7 and then 2. Bf5.

Am I missing something? If the mate in 2 is correct, is it common/normal for a problem to request a mate in 3 when a mate in 2 is available?
After 1.Ne7 Black has 1...f5, stopping the immediate 2.Bf5#.