Jemma did not take kindly to people touching things they shouldn't. Because really, it was proper etiquette. Then again, most of the scientists had a bit of healthy fear of Jemma thanks to the whole...shooting the previous director (with an icer) because of an Orange County situation, or the fact she would assign papers if people were idiots. Add in her training with Natasha and well...she wasn't nearly as demure or helpless as she often appeared to others.
"I don't see why not, but we would need to check." But really there was no reason why the two couldn't be combined. It was all about utilising the skills of those there. It was why Ruby did engineering but also was sent out on the field because she was also a fighter. Jemma did medical (even if she wasn't an official medical doctor yet) because she had field medic experience.
"I mean to be fair, how often to the bad guys actually say that they're the bad guys? But yes. We are. And we would certainly be happy to have you."