It's actually referring to the actual level of the item you're trying to equip, not the ilvl. As in if you're wearing level 70 Scaevan gear that has an ilvl of 390 (400 if augmented) it won't let you use a glamour prism on the first dungeon's gear that is level 71 but has an ilvl of 370. Same with the second dungeon that has level 73 dungeon gear but an ilvl matching unaugmented Scaevan gear.

So long as the actual level of your gear is higher than or matches the actual level of the gear you're trying to glam it doesn't matter what the ilvl of the gear is.

Source: Spent multiple hours trying to figure out why I couldn't glam level 63 Shisui legs over my level 60 Shire legs, realized why and facepalmed myself.