The speed used depends on the route requirements. I may need the greatest distance out of my diversion speed (max) or I may need the lowest fuel requirement (LRC) or there may be other considerations.
Consider a route where the ETP between en-route alternates is at a distance equal to max speed for two hours (ETOPS120 example). Then I have to plan using max speed and start with enough fuel to go to the crit point then divert at max speed.
It may be that if I divert from the same point at LRC I will arrive with more fuel but the diversion will take more than 120 minutes.
So it's not true to say that if you divert at a different speed you always WILL run out of fuel.
However, If your ETOPS distance was based on LRC and you divert with a different speed then you better use the correct speed!
Best bet is to have an idea about your routes and the speeds your company has chosen because it can be completely different from route to route as well as airline to airline.