Yes, in theory your thinking is correct and as long as the installation is up to code (which it may be) in your area, you should be fine. Remember that local electrical code inspectors can vary in their understanding and interpretation of electrical codes, which can vary a bit by location.
The one issue for the discussion is that a 20-amp receptacle has a physically slightly different plug configuration which implies it is connected to a 20-amp circuit. Someone may be misled when they see a 20-amp receptacle thinking they can use a 20-amp rated device. Of course, the 15-amp breaker would trip if the 20-amp device were to overload it so there should be little to no risk of an overload causing a fire.
**Disclaimer-I am not a licensed electrician**