Labeling of "multi-factor" is confusing

[utsecnet]

63b 4.3.1 states at the first bullet point that within AAL3, a multi-factor cryptographic device (MFCD) is allows as a sole device to provide authentication to a verifier. However, these types of devices only transmit one factor to the verifier. You are simply unlocking that factor with a second factor. This is like taking your house key and putting it in an exterior safe box that requires a code combination to retrieve the key. Does this make your home a 2-factor protected home? No!

If you look at the difference in comparison to using A SF crypto device (SFCD) together with memorized secret the unlock process looks like this:

1. Claimant authenticates by providing the verifier with a password (1 factor)
2. Verifier sends a challenge to the authenticator (SFCD) via API.
3. Authenticator signs the challenge and returns the signed assertion to the verifier via the browser (2 factor).

In that example, the verifier is requiring reception of both factors before authentication is permitted. If we look at the MFCD process it looks like this:

1. swipe your finger/enter PIN on your MFCD
2. That action unlocks the crypto key (the verification happens on the device, not the verifier!)
3. Crypto key sent to the verifier, which then grants access (Only one factor is sent to the verifier!)

Why is this permitted? Is my reasoning wrong?