Vapourising essential oils to combat MRSA sounds like a good idea, used as well as and not instead of good cleaning, as the article says.
Many common essential oils are strongly anti-septic and anti-viral; furthermore since each one is a mixture of many different compounds (typically various aromatic ketones, aldehydes and esters)it would be hard for the bugs to develop resistance. Being highly concentrated and very volatile, it wouldn't feel like 'having oil sprayed into the air', and anyone with asthma would find their breathing unaffected or improved. (Yes, I work with essential oils in my life outside the NHS!)
Will this idea go into general use? No. Hospitals are nervous of complex natural substances, they prefer simple synthesised compounds, where any risk is underwritten by the manufacturing drug company.
Interestingly this only seems to be the case in the West; in China and India they seem to be able to use natural medicine alonside synthetic medicine without any problems.
Moira the Witch Doctor (part-time)