As far as I can discern, the most effective counter to a status ailment, given time, is the Resistance skill. As this is a skill every character or party member will have to roll against some day, it's handy to have around; as I recall, using a skill you don't actually have incurs, unless you've got the right Talent, a -2 penalty.
The Resistance skill uses the Ego stat. A character with a high ego stat might never notice the difference, I'd have to ask Peter or Hewitt, but a character with a low Ego and no Resistance skill is probably going to have a lot of problems. Therefore, if I'm not playing a martial artist or cybernetics buff, which makes Ego one of my low stats, I tend to ramp up my Resistance skill. The same applies to my lancemates.
That said, it would be rather nice if doctors had an effective solution to the chemicals that cause burn status ailments.