I think the description of this, such as Bitcoin Magazine's Tweet, as it being KYC-Free are inaccurate. I don't think Edge will let you sell bitcoin (to acquire the USD for this) without doing KYC on their wallet.

Your personally identifiable information (PII) certainly must get transferred to Iona and/or the bank (Patriot Bank N.A., issuer of this Mastercard). And even if it doesn't, should Edge be given a subpoena, they would have the PII for the account that funded that Mastercard.