The results are the same if you calculate using either equation. I don't know the technical difference between the two but they give the same answer. The simpler way is to calculate by reload time.
There is no technical difference between the two equation because if you simplify the larger equation they are both the same. You haven't actually done the calculation in any different way, so you did not prove anything because you haven't calculated it they way it should be if the actual reload TIME was reduced.
Picture the reload time a bottle with the capacity of 1 liter. Picture the reload speed to be someone pouring in water at a certain rate, so if it will take that someone 4 seconds to fully fill up the cup his reload speed is 0.25 bottles/sec.
Now if we take muse's saying of decreasing the reload TIME by 25%, that would mean that they have two options:
1. actually decrease the capacity of the bottle by 25% - so instead of 1, you would have to fill up 0.75. Now I have to say, this option is completely idiotic - it means that if you have weapon that it's reload time is so high compared to stamina usage time so that after you finish the use of stamina, you still have not reached 0.75 - you have less than that AND then the cap is raised back up to 1 so effectively stamina had no implication at all. A different scenario is that you would activate stamina a fraction of a second before you would have reached 0.75 - meaning the cap would be lowered to 0.75 and the reload the reload would be instantly done - with practically 0 stamina usage.
Obviously the first option is not the case, as determined from observations in-game, so it brings us into option number 2-
2.When saying that reload time was decreased by 25% the people actually mean that you still have a bottle of 1 liter, but the guy who is pouring is actually pouring it at a faster rate so that it would fill up as if it would have been a bottle of 0.75 liters at the previous, slower rate. So, in order to get that going in the new speed - the speed will have to be(as already calculated by ZanC here) +33% faster.
Now, there is actually a 3rd option that is competing with option 2 on the title for the truth, which is that the developers don't actually make things so complicated and tangled up like in option 2, but they have actually got confused with the terms of reload speed and reload time. Which would imply, that it is most likely an increase in reload speed.