They just say Bluetooth. They don't say "Version x.xx" or "A2DP" or "802.xx" or anything, either on the hosting device, or on the portable device. The television and the headset both just say "Bluetooth."
The box, the advertising, the instruction manual, and the setup menu that you look at in the store of the model 800E and the model 850E are identical. But with the model 850E you do not have to buy a transmitter. The headset pairs with the television instantly. With the model 800E you do have to buy a transmitter, because the headset does not pair with the television.
So with the model 850E the "actual hardware with a interfacing radio is native in the device," while with the model 800E it is not, and yet the wording on advertising and on the product box is identical. How is this not consumer fraud?
You cannot "check this before buying is to look at the specs to which Bluetooth or WiFi standard the device is actually compatible with," because those specs are not provided either in the advertising or anywhere on the box the product comes in. At least not with these Sony products.
"Should the label that touts Bluetooth support also have print saying, 'Dongle required/not included'?"
I would say they should not, because those devices do not, in fact, support Bluetooth. They have USB, RCA or optical ports that allow a transmitter to be connected, and the transmitter supports Bluetooth. Those ports can also support a vast array of other types of electronic devices that have nothing to do with Bluetooth. Saying that they support Bluetooth, even if they admit that a Bluetooth transmitter is required to do so, is fraud. Nothing in their hardware supports Bluetooth.
Again, if they do not have an internal Bluetooth transmitter, if their internal electronics cannot pair with external Bluetooth devices, then they are committing fraud by claiming that they "support Bluetooth."