Cauchy, I believe you are correct. I looked it up too 18 months or so back. According to what rules I could see there was no specific restriction in BAEC or CoC to avios only bookings. I was GGL at the time and queried it. I did get something in writing from BAEC which confirmed their position in my specific case (although my request they quote the specific paragraph and rule wasn't met).
However, coincidentally, an alternative direct routing came up via a schedule change, wholly on BA metal. So I called back and requested the re-route and it was granted; I even got some avios back.
As things worked out I didn't press the re-booking shenanigans ... I've now diversified away from avios on North American routes because of this, amongst other things, and the AA/BA propensity for awkward schedule changes.