I've watched my positions with D4F go way below my stops occasionally and whipsaw above and below several times before being taken out of the position. However, I have generally found that the stop price (or close to it) was honoured even if the current price was quite far on the negative side. I suspect that because they are not tied to the underlying prices, they have some flexibility in deciding to honour a stop even if the price has subsequently gone the wrong way.
With IG Index, I had one trade where their software wouldn't respond to my order to close the position. By the time I got through on the phone, it had gone much further against me. However, they honoured the price I would have got if the software had worked. More proof that they can be flexible when they want to be.
It probably helps that I'm not a punter who is taking money from them on a regular basis.