You said best offer was 1133.90. If buy order is placed at $1134 with HFT firm they must either fill the order at 1133.90 (the NBBO) or pass it on to an exchange that has NBBO.
If you are arguing something else happens then you need to explain it clearly step by step in a timeline.
2. Trade gets routed to an HFT who will fill the trade
3. HFT notices a spike in GOOG interest over a few seconds and starts buying at 1133.90 driving the price up to 1134
4. HFT fills your limit order at the best price of 1134 which they themselves hold.
Despite what the other commentators here have said, limit orders are less safe than market orders to market manipulation. HFT's will buy up all that dumb flow with limit orders and then essentially run the prices to the limit orders in their favor.
At the beginning of 3. does the HFT have your order or are you saying that the market moves before the HFT receives the order?
As far as I know the first case is prohibited (actual front running). I don't see an obvious problem with the second case though there might be subtlety that I am missing.
If you are arguing something else happens then you need to explain it clearly step by step in a timeline.