I do agree that (as is so often the case) the directive is not specific enough to determine whether the Italian interpretation is correct or not, though I can provide some context from the German side as provided by the ministry of finance: "Eine lückenlose Abfolge der ausgestellten Rechnungsnummern ist nicht zwingend"[1] (~ "it is not required for the invoice numbers to be gapless"), which directly contradicts the Italians as far as I understand it.
[1] https://www.bundesfinanzministerium.de/Content/DE/Downloads/... - p. 522, 14.5 (10) 4