I would have to disagree with you about that, Joe. Sending pieces of the 'true cross' to various churches to be venerated is quite different from destroying a piece of the true
cross. Of all the relics, the true
cross was considered the most sacred, and to burn even a piece of this most valuable object in the world would be unconceivable. What's more, by this time, there were ways to 'transport' the sacred power of a relic, or a saint, to an object - by touch or by proximity, so to create a token blessing such as these, there was no necessity to destroy a piece of the relic by burning. Check out Gary Vikan's 'Early
Byzantine Pilgrimage Art', which will be worth your time reading.
I have also read this theory only in sales descriptions, and I think it is just uncritically copied from one dealer to the next.
Still, I'd like to know the source.
Regards
Gert