I mean, for the people of the galaxy, Palpatine was just a politician past his middle ages. How could this man have survived against four Jedi Council members in his office while “unarmed,” say that the attempt “left him scarred and deformed,” and people believe in this?
The short answer is that we don't know. Certainly the Emperor had his own guards and clone trooper escorts but beyond the pronouncement that the Jedi had attempted to assassinate him, there's no explanation of what the general public were told about the event other than the Emperor had dueled with the Jedi and somehow overcame them, albeit at the cost of being injured.
Note that the overwhelming majority of the public had little or no understanding of the powers of the average Jedi and might think that his success was odd, but not necessarily realise quite how drastically unlikely it was that a lone, unarmed non-force-user could kill three armed Jedi.
There were many stories about what had occurred that day in the chancellor’s office. The official explanation was that members of the Jedi Order had turned up to arrest Supreme Chancellor Palpatine, and a ferocious duel had ensued. The matter of precisely how the Jedi had been killed or the Emperor’s face deformed had never been settled to everyone’s satisfaction, and so Tarkin had his private thoughts about the Emperor, as well. That he and Vader were kindred spirits suggested that both of them might be Sith.
Tarkin often wondered if that wasn’t the actual reason Palpatine had been targeted for arrest or assassination by the Jedi. It wasn’t so much that the Order wished to take charge of the Republic; it was that the Jedi couldn’t abide the idea of a member of the ancient Order they opposed and abhorred emerging as the hero of the Clone Wars and assuming the mantle of Emperor.