The markov property imposes a form of unpredictability on price dynamics within financial models. As you noted, if this was exactly true, technical traders would effectively be wasting their time.
Now, there is a bit of a problem in what you wrote about technical traders. They believe that some price patterns can predict future stock prices, but this is very different from having established this predictability on sound statistical ground. My experience talking with people who engage in analyzing price patterns using concepts such as resistence and support levels, candle stick patterns, trend lines, etc. is that they are using a very fuzzy rule. If you ask them to make those rules explicit, they would all fail to do it which means by definition that they are unable to run backtests. With enough randomness and enough such traders, even in a Markovian world, a handful would be bound to be regarded as geniuses just as running a gazillion backtests on a limited amount of data is bound to turn up arbitrarily high Sharp ratios on a trading strategy, again, even in a Markovian world.
So, who's right? Well, I strongly doubt that financial markets would organize themselves to magically produce exactly Markovian dynamics. On the other hand, people trying to take advantage of non-Markovian dynamics would presumably push prices most of the time towards being more Markovian. That point is precisely why I think your prior should always be that price dynamics obey the Markov property -- in fact, I think that should be a pretty strong prior.