If MRSA isn't airborne then why can you get it by breathing in droplets from sneezes and coughing?

That would be so rare as to be almost impossible. You'd have to have stuck those droplets up your nose, and had low resistance (since staph lives all over your body including your nose), and had some sort of cut to let it into your tissues. In other words, it isn't airborne.

MRSA is a resistant strain of the staph we all encounter 24 hours a day. Some people even have the MRSA strain on them with no ill effects.

Studies in the UK have put HEPA filters in hospital rooms and found that MRSA was decreases by 74 to 90 per cent. It has long been considered that MRSA is airborn contamination but nothing proven conclusively.