The N can run regular fuel. This was right from the dealer when I bought it and confirmed in the owners manual.
Albert Bierman also said in interview it can safely run on regular unleaded fuel but will do so at a reduced level of performance. In my opinion "reduced performance" = not doing it but it can be "safely" done if required.
Also motortrend published and article about the Veloster N fuel economy and said:
"That’s also only half the story. You see, unlike the Type R, the Veloster N doesn’t require premium fuel. Even though it’s turbocharged, it runs on good, old-fashioned 87-octane. By the EPA’s calculations, that little detail means you’ll save about $1,750 USD over the next five years." (
https://www.motortrend.ca/en/news/2019-hyundai-veloster-n-gets/)
Mine on the other hand will only ever see Ultra 94

.
Also, for them to say "no modifications allowed" is bollocks. First off you own the car after purchase, not them. They cannot dictate what you do with it through any means.
Even from a warranty perspective, a blanket loss of warranty due to a modification is a violation of consumer protection Acts, specifically the Magnuson-Moss Warranty Act of 1975.
"Although many dealers would have you think otherwise, simply having an aftermarket part or modifying your vehicle cannot void your warranty." -Edmunds.
There is a requirement for the warranty provider to prove that the failure was a direct result of the modification in order to legally break a warranty contract. The only exceptions being improper use and negligent maintenance practices which both must be outlined and defined in the owners manual and warranty information.
I checked the paperwork I just got with my N and it actually states that warranty claims may be denied if the failure is a direct result of modification.
I only know this as I have been a long time modifier of vehicles (18 years and not a single bone stock car to be had) and have had a big fight with Mazda (which I won) when they tried to deny a warranty claim because of a modification completly unrealted to the problem. They will always try to deny your claim but if you fight back they end up not having a leg to stand on in most cases.