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Accessing password hashes already in a DB is not the same as preventing, during account creation, the reuse of a password known to be compromised.

If I'm not mistaken it's all done using cryptographic schemes that leak neither the password nor the hash.

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This is true. The story as written probably didn't happen with HIBP's database. Troy Hunt's database only includes SHA-1 hashes, and passwords in your own database will be hashed with a stronger algorithm (hopefully) and salted (hopefully), so you can't do a simple hash-to-hash comparison. The way to do a HIBP check is, when a user signs in, you hash their password in the way HIBP expects, and check that against either their API or against a local copy of HIBP's database, and if a hit is returned, you give them a nice message and direct them to the password reset flow. There's no easy way to use HIBP's data to identify users with compromised passwords until users actually try to log in.

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