Given that variable bit-rate VoIP can reveal words spoken from bitrate alone[1], I would be very cautious about their claims.
[1] https://www.schneier.com/blog/archives/2008/06/eavesdropping...
[1] https://www.schneier.com/blog/archives/2008/06/eavesdropping...
A more practical side channel attack would probably be through radiated emissions over the mains power. However if you're willing to go that far, a laser microphone is much more effective and simpler.