I don't know that this holds true for EVERYONE experiencing this problem, but I'm noticing that several people (first of all the OP) have made red flag comments about the screaming ultimately getting the child what they want.
Examples:
"If I set her food in the wrong chair she will scream and howl out until she is in the chair she wanted to be"
"She clamors for choc milk or candy at Whole Food and whereas I used to agree, now I practice saying no more often,"
"I used to always pick her up and hug her and try to see what she wanted."
If screaming holy hell gets you what you want, even once, it becomes a viable method for getting other things.
We've made a major effort emphasize that screaming/crying is NOT an acceptable form of communicating what you want. It's AMAZING how my DD can go from 60-0 when we calmly say "I can't understand you when you're whining/crying." In an INSTANT she stops all the drama and very clearly and calmly states what it is she was howling the second before. Once that happens then we can actually talk about what it is she wants and have a much greater likelihood of being able to calmly negotiate it. She doesn't always get the thing she was howling for, as it may just not be a reasonable request, but she HAS to make herself understood calmly and politely.
I really try to avoid concerning myself with what other people think in terms of public parenting. I hope that people with any sort of sense will understand what's happening if I have a howling small person and I'm attempting to calmly deal with them, and honestly, if you DON'T get it, and you're THAT put out, tough. It happens. My concern is with parenting as effectively and consistently as possible in a fashion that I believe is constructive. If I try to please the adults around me instead of focusing on doing my job, I'm doing my DD a disservice.