I don't think Morgan exagerated, he gave the news in a very tabloid way but it was a fair assement.
Luffy was already building a reputation as a crazy ass kid (cleared up the East Blue, was involved in Arabasta, attacked a World Governament site and declared war on it on Ennies Lobby, punched a Celestial Dragon in Sabaondy, infiltrated Impel Down and capitained the break out, and then he shows up at the War and his family relations are revealed). All of this in about a year (well, according to some estimates we can make). And then he disappears for a couple of years. This is already a nice story for a newspaper to follow.
When he reappears, he announces it to the world by smashing half a douzen of Pacifistas, takes Fishman Island from Big Mom claiming it as his territory, makes an alliance with another supernova, who became a shichibukai, to defeat another shichibukai, and gets an Armada of allies. Then he allies with yet another supernova, plot and attemps to take out Big Mom, making good on his promise from Fishman Island, trades a couple of blows with her, wrecks her territory and takes out two of her commanders.
Sure, we know more details of the events, how he needed Nami's assistence to figure out how to beat Cracker, how Luffy vs Katakuri was really really close and he wasn't in a level capable of actually defeating Big Mom. And that's just in WholeCake but that is not the public perception. To the world he showed up, said he was gonna beat Big Mom and actually did serious damage to her turf, this just after Uroge attemping to do the same and getting way worse results. And that's because of the alliances, Luffy is getting the other members of the Worst Generation under his umbrella, more than having the Straw Hat fleet, like Whitebeard had several smaller captains under him, he's getting the top-dogs of a generation, like the Rocks Pirates.
We saw Blacbeard becoming an Emperor by taking the power (and territories) from an Emperor he killed so they were still 4 Emperors, but there's no mathematical rule to how many islands, or crews, you need to have under you until you're claimed an Emperor or that the number must be 4. Luffy did not need to take out an Emperor to be declared one, he simply needed to show that's a possibility, that he has enough power to actually challenge their rule and impose his own.