I don't get why you insist on calling it blinding, since no message is hidden here. Using commitments to cooperatively generate a random bitstring is pretty common.
I was referring to the two move protocol in Adam's message (apparently originally by hhanh00 but lost?). not the ordinary commitment there by Sergio. And I refereed to it as blinding because it makes the numbers in the transcript statistically uniform to a party who doesn't know the secret, and because it's similar in construction to a full blinding scheme-- effectively it's blinding the nonce used by the signer but not the message. Thats all.