I´ll take a run at this...
Company 3 still needs to charge IGV to company 2 on the rental by law, since the service they provide is provided in Peru. They are evading tax by not providing company 2 with a factura.
Company 1 could enter into the "off the books" game, but they would also be party to tax evasion. Company 1 could (and should) charge the tourist IGV on the service they provide (including their markup) and Carlos can claim a refund when he leaves the country. Company 1 needs to register in the "Registro de Establecimientos Autorizados" in order for this to happen. (see https://www.perutributos.com/noticia/de ... xtranjeros