Äh...
...if you get a quote from a BROKER, it is NEVER from the broker, but from the exchange. There is no sense in having multiple brokers if you work against the same exchange, because - unless ones systems suck - they will show the same data. This is also why a broker gets paid by buy/sell... the price you get is the ORIGINAL price from the exchange, official, tracable, debatable (if you do not like it) with proper procedures. So the broker has to be paid separately.
If you get stopped out, it is because the exchange computers (in most cases, I am not sure anything is still run manually) will decide that your stop got hit, and it will not matter what broker it was entered through.
A broker can not alter the price, unless.... it alters it on the exchange.
In some cases (I will soon use Mirus) the data feed you get from them is even the unfiltered exchange data feed
Brokers do NOT get involved at all in determining the price.