Ambassador Fox and his aide beam down to the planet even though the "Enterprise's" deflector screens are up - it was stated that transport could not take place under those conditions. However, Mr Scott had moved the Enterprise further out into space, in a wider orbit, where sonic disruption was impossible. The locals even acknowledged that they could not attack the ship. Therefore, it is reasonable that screens could be opened briefly for transport.
The goof item below may give away important plot points.
When Spock rescues Ambassador Fox from a disintegration chamber, the door to the chamber is opened. As they back away to destroy it, the door is immediately closed. (Obviously stock footage of the first chamber destruction.)