Most Arabs I've ridden (and I grew up with 10+ on the property, they were my mom's breed of choice) naturally carry their heads high and can be hot. It's all workable though. The nice think about horses are their heads are adjustable, as is their carriage. My 3/4 arab I own now likes to roll peanuts if you let him, but also goes on the bit nicely. He didn't start out this way though. He'd try and thunk you in the face.
Arabs certainly can be opinionated. They're free spirits. Which is why I've grown to love them so much.
I agree with WSArabians to an extent. It most definitely can be a training thing, and it usually is, but it IS a trait most commonly seen in high headed breeds. It can obviously be trained out of them, but it does take work as the natural inclination is to hold their head high and when that combines with the sensitivity and any bad training or a coarse rider, they are quick to show their displeasure.
You just don't typically see the head flipping thing in non-high headed breeds because they find different ways to voice their displeasure based on conformation. For example, bad training makes it darn easy to make a tough mouth on a stock horse for example. Many stock horses are a lot less sensitive, and you see all sorts of crazy bits on barrel horses just to control them. You rarely will ever find that problem in an Arabian, regardless of training, you can almost always throw them back on their haunches into a halt just from their inability to disconnect from their sensitivity.
Obviously it's a case by case bases and no stereotypes intended, but it gives a comparison as to why you may find a flippy head Arab or an impossible to stop stock horse for example. Breed and conformation tend to bring out generic ways of evasion when put in sticky situations.
None of my 3 Arabs toss their heads, nor are they "hot" horses. I've seen plenty of QH's running around with ew-necks and head tossing, I believe its all in how they've been "trained" by their riders. A lot of people (no offense to anyone) ride these horses with a heavy hand and they are the reason the horses like that (it may not be you but riders before you).. Kinda late reply but just wanted to add my 0.02 ;)