I have faith that they'll do a fair job. It wouldn't make sense, and it'd be poor journalism, for the BBC to run an anti-vegan smear campaign. Plus, I get the impression that they're looking to highlight performance athletes, which connotes a healthy diet.
That said, while Martial Arts covers a lot of territory in terms of the spectrum of the styles, I think it's relatively straight forward in the types of athletic endeavors the term entails. To be clear, it is those sports, styles and forms relating to combat (hence the word martial). While Tai Chi wouldn't seem to be a martial art per se, there is "combat Tai Chi" and the forms are based on combat-related stances.