Haven't watched the video yet, but I think this capability was leaked by VP Kamala Harris during her recent interview with the Late Night Show [0]. She stated she doesn't use wireless headphones because she's been in security meetings and knows they're not safe.
[0] https://youtu.be/BD8Nf09z_38 (Timestamp 18:40)
Disclaimer: This comment is not intended to be political - I don't care about the specific party she's part of.
Out of all the people I would trust on the matter, Kamala Harris doesn't certainly end up at the top of my list, for reasons such as this one: https://youtu.be/O2SLyBL2kdM?si=Zq-EN8zxj4Y_UCwI
You also don't need to be in classified meetings to understand that Bluetooth/ BLE (and specifically the way most vendors implement the spec) is not as secure as other more battle-tested technologies