There's a lot of misinformation about 'pairing' and powertouch and other movers employ a single frequency pairing method , you put the receiver into listen and learn mode and if a handset transmits a specific command including an ident code ( serial number of the unit) on one of several frequencies then the receiver acknowledges that, exits learn mode and only receives commands on that frequency. Other hand units which also transmit on that frequency may interfere with the command string and initiate a response from the receiver - hence the odd actions the mover reported.
I don't know if the handset sends out it its unique serial number with every command string, which would help reduce the receiver misinterpreting a command string, even if it did, a specific burst of radio signal from a second hand set mid command string may cause the incorrect action ( timing would have be pretty precise, but not impossible)
Bluetooth 'pairing' is a lot more complex as bluetooth comms involves frequency hopping during each command string ( message) sent.
Which frequencies are to be used (out of the available band(2.4 to 2.8GHz) and their sequence they are used in during the message is decided between the two units during pairing( often a code is sent which has to be confirmed), During transmission and reception there is a lot more handshaking ( comms backward and forward) to ensure the correct 'packets' of info have been received and from the correct (paired) device , This way it is a LOT less likely the messages can be intercepted ( If you tuned a radio receiver to one of the frequencies, you would only receive only part of each message) also it means interference from another bluetooth system is less likely and if a full command is not received the request is rejected and the receiver asks for a re-send.(As Sheldon Cooper says , everything's better with Bluetooth). Reich movers have the option of fitting a Bluetooth dongle which using the free Reich app on a smartphone makes their system even more robust. Powertouch may have a similar option on their kit , but I have not come across it.