Anyone can move the market if they got enough cash to do it. The question comes down to 3 qualities associated with moving the market:
1. how quickly they can move the market
2. by how much
3. how long can they keep the market at a price range
HFT can certainly do all three. It just comes down to the measurement for each of the three.
Btw, HFT doesn't mean low latency trading. So holding something in millisecond timeframe doesn't mean that person is HFT.