FaceTime Failed: Person Not Available

Question

Consider an iPad 2 using WiFi attepting to make FaceTime calls to users on an iPhone 4. Each contact has their phone number defined under the iPhone tag (as opposed to Mobile).

Whenever attempting a FaceTime connection, FaceTime attempts to connect, and fails with the error:

FaceTime failed - 'Person' is not available for FaceTime.

Measures attempted:

• close FaceTime from running apps.
• disable & re-enable FaceTime from Settings.
• confirmed the device's WiFi is active & enabled.

I've seen the 'solution' of "reset all settings", but suspect that's overkill, and likely won't work, as reported by lots of other users.

How can this error be avoided?