The slower mission times are for chemical rockets where we barely get out of Earth orbit with a small rocket engine. SpaceX Starship can refuel after reaching orbit to enable faster orbits (straighter and less looping paths) to go to Mars. This makes 90 day times each way easy with chemical Starship and even more wasteful but still chemical rockets to Mars in 45 days each way.

This is calculated by Ozan Bellik.

In 2033 there are opportunities to do a high thrust ~45 day outbound transit with a ~10.5km/s TMI (trans Mars injection). If you refill in an elliptical orbit that's at LEO+2.5-3km/s then the TMI burn requirement goes down to 7.5-8km/s. A SpaceX Starship with 1200 tons of fuel should be able to do with roughly 150 tons of burnout mass. This is enough for ship, residuals, and a crew cabin with enough consumables to last a moderately sized crew for the 45 day transit. The trouble is that once you get there, you are approaching Mars at ~15km/s.

One way to solve this would be to powerbrake to 8.5km/s and aerobrake from there. This needs an additional ~6.5km/s, and the most straightforward way to solve that is to send a fleet of expendable tankers alongside the crew ship and refill en route. This would call for 5 or more fully filled 2000 ton tankers in elliptical orbit. SpaceX could do it.