What a pickle. Please know that I very much agree with you on this one - but, think of it this way. When we think we are good at something and someone else bests us at it (as you did with your approach vs. hers) it can bring out a very unpleasant reaction. Reacting the way she did is one way people often try to save face when they realize that they were not necessarily right.
On issues where it isn't really a matter of life and death, try the, "Thanks for the tip" (not said in any sort of tone) approach which gives the other person the satisfaction of being heard but doesn't obligate you to actually TRY what they are suggesting. This is a great way to avoid things becoming fights.
Something I like when it comes to arguments/fights is this, "How many people does it take to have a fight?" Answer - two. It can only be a fight if you engage with her - if you don't, she's just talking to herself.
Chances are she would right exactly what you did above, just from the other side of it. That doesn't make what she said or did right (or wrong, for that matter), but when we take the step back and realize that, it can help us figure out the best way to approach the situation to keep things from blowing up.
Kudos to you for taking the gentle approach