According to the article, it shaves 25% off the fuel costs Yes, by the facts and speculation reported in the article kindly submitted here, the headline phrase

According to the article, it shaves 25% off the fuel costs Yes, by the facts and speculation reported in the article kindly submitted here, the headline phrase "on the cheap" is plainly wrong, and "anytime" is an exaggeration, as the overall trip time will tend to be longer for most such missions. The article also notes, "The burn-free, capture altitude is also quite high—some 20,000 kilometers above Mars, far beyond where science satellites set up shop to scrutinize the planet up close. But taking along just a little extra fuel can then gently lower a ballistically captured spacecraft into scientifically valuable, standard orbits of around 100 to 200 kilometers like those achieved with Hohmann transfers—or even onward to the Martian surface for a landing." So one part of the article says that the mission will take less fuel (to leave the vicinity of earth), while another part of the article says that the mission will have to carry along extra fuel (in the Mars exploration modules) to arrive at a location where useful science can be done. The bottom line here is that these missions will still be about as expensive as current missions, and manned flight to Mars and back will be staggeringly expensive.