I have been an insulin dependant diabetic for almost 27 years now, and I actually think that the issue of injecting in public is a lot like the issue of breastfeeding in public. Do it but try to be discreet. Try your best not to let the nipple or needle show but don't freak out about it.
Personally, if everybody in the immidiate area knows I am diabetic, I will just do it right there at the table, sometimes making the joke "I'm just going to take the drugs now". If I am in mixed company or around people I don't know well, I won't go so far as to find a bathroom, but I will go to a corner and do it there. The exception being, if it is one of those rare occasions when I am wearing sleeves that are too tight to push up, and I will actually have to partially take the shirt off.
And also, I would like to point out that sometimes, being discreet can cause more attention to be brought to yourself than no such attempt. If you make a big deal out of it, asking really loudly where the host would prefer you to go to inject the insulin, making a big fuss about it, everybody will stare at you and think "poor you", when, especially if you have lots of practice, you can, even with a syringe and bottle, just do it so quickly that no one even really notices until you are done. Believe it or not, I have been in several situations where I was eating a meal with people who knew I was diabetic, and we would all get up to leave the table, and one would say "don't you want to take your insulin?" and I said "I already did", and they were amazed they hadn't noticed.
And I wonder if this lady just didn't have enough practice yet. Is she recently diabetic? You need a lot more space to work with to make sure you do it right, until you get the hang of it. Though that does not excuse her behavior, of course. If she really was so unpracticed that she needed to expose herself, she should have gone into a bathroom or out to her car or something.
As for injecting through clothes, I know some people do it, but I don't, but the only reason is that I don't want to get blood on my clothes.
Otherwise, I totally would do that.