In my opinion a plot surprise cannot be sexist. A book cannot be sexist. Only an author can be sexist.
Your story is something that happens in real life. That's undeniable and its fair game for literature. But it is a contentious issue. So if you want to write this story, you need to be very aware of the arguments around it.
You may not feel like you're making a statement on rape or women who accuse men of rape, but you clearly feel that this story is important and needs to be told. Why? Perhaps you do have something to say about it? And I think you should.
Because if you don't, then you're just using it as a plot device and that, in it's way, is a statement in and of itself.
False rape accusations are part of a complicated social narrative. If you write a book that presents this situation without thinking about where your sympathies lie, or without reference to that real-life social narrative, then you risk it becoming interpreted in ways you didn't intend.
I'm afraid, whether you like it or not, if you write it you're making a statement. Or at least a comment. Because you're not describing a real thing that happened. It's fiction. You're making choices.
Which is fine, make your choices but know why you're making those choices and be able to defend them.
More practically, I think you can ignore the advice that a reveal of the character's dishonesty later in the book would be a let down. Particularly if you've built up a good bit of sympathy for this character, a punch in the gut is no bad thing. As long as its earned, you can do what you want.
Essentially, this is all going to come down to how you handle this issue in your story - how clear are you in your thinking about it. And how skilled a writer are you to be sure you're sending the messages you want to send?
Hope that helps
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The Andaman Sea, the Andaman Sea, I'd like to be, on the Andaman Sea.