That is partially false... The incontestable part is that you may beg to differ () but some Eastern emperors recognized Charlemagne and his successors as Western emperors, confer, for example, Michael I by the Pax Nicephori.
Αctually with Pax Nicephori Byzantine Emperor recognised Charlemagne's authority in the West but as a "Rex" (aka King) and not as an "Imperator" (Emperor) thus technically making Charlemagne his vassal... In reality Byzantine Emperor had no authority over Charlemagne and his successors but Pax Nicephori was written in such a way in order to refuse the imperial title to Charlemgne. See how Emperors used to call Holy Roman Emperors in correspondence or during ambassador visits... Always with the inferior title "Rex" and never as Emperors...
Besides that ERE Emperors possesed the Western Emperors regalia since 476 when Odoacer shipped them to Constantinople thus recognising Zeno as Emperor of a "de jure" reunited Empire... And Charlemagne knew that without the Byzantine Emperor's recognition his title was hollow...