(I don't in any way own this document).
I acknowledge that the situation with Bluetooth peripherals is complicated† and accept that there are probably a bunch of vendors that are unsafe to use. It might be reasonable to simply require Apple peripherals --- not because they're the best, but because Apple is more accountable to peripherals security than most other vendors are.
On the other hand, what we can't reasonably do is create a Bluetooth Keyboard Product Guide in a simple set of security recommendations. Not only will it not be effective, but it will discourage the audience, who will fall back to their previous insecure configurations.
So I'd ask to what extent we think Bluetooth sniffing attacks on journalists are a spy movie threat. No matter what device they use, simply by using a wireless device as an input, they're exposing those inputs to timing as well. But then, as well, Apple's software update could be targeted too.
The basic idea behind the "use a Bluetooth keyboard recommendation" is, I presume, to convince people who would otherwise use computers to do sensitive work to instead use an iDevice. That's a very sound security principle; those iDevices are far more secure than the median fully-functional computer.
If I had to pick between telling a journalist to use a random Bluetooth keyboard with an iPad, or use a Macbook or Thinkpad, I would have a hard time deciding, but I think I'd ultimately go with the random Bluetooth keyboard --- there are too many different ways the computer can be undetectably (to a typical user) owned up, and only one fairly elaborate scenario where the BT keyboard will screw them.
What I'm learning from working with at-risk normal users is that a lot of security steps we all take for granted are simply not on the table for the people who need security the most.
† Way more complicated than the people claiming "Bluetooth keyboards are trivially sniffable" are letting on