Peer approval schemes are usually implemented as trade efficiency measures. A one sided peer approval would make it easier to import, while not making it easier to export, causing a delta trade deficit.
Obviously any authority that takes its job seriously makes decisions based on facts and not blind trust.
We have no intention of dropping our standards to US ones, but they are welcome to follow our lead. (Or don't! It's up to you, just don't make it our problem!)
For a country which has a sufficient approval scheme, they lose little by choosing not to trusting an insufficient approval scheme.