Someone has to sit next to the sick passenger. Whether its the OP or the original neighbour, thems the breaks and thats all part of air travel. I don't think i would have the cajones to say "oh no, we are special snowflakes who don't deserve to be contaminated".
As to whether she was really sick or not, that's not really up to yours to judge. I once had a very scary asthma attack shortly after being seated, but was able to manage it fine later. My husband *thought* he had montezumas revenge while on business to India, and had this realization just shortly after take off. But, he ended up fine after 15 mins into the flight. It can be really scary to have a health issue around the time of take off, when you don't know "is this going to get really bad, or is this just a momentary thing?". I've had it go either way. It was smart of her to ask to sit closer to the bathrooms (just in case) and it was wise of the FA to place her there.
If there's anything such thing as karma, maybe the person who denies a potentially sick passenger faster access to the bathroom will get stuck in the back next to a really sick passenger who doesn't have fast access to the bathroom. :P