But let us disregard here for a moment that Nadal used a slight misstep of his here to call for an unwarranted time-out and disrupt the rhythm etc., and let's concentrate on the application of the rule and the rule itself.
I don't agree with you entirely: either they applied the rule incorrectly, or there is something wrong with the rule - or both. There was nothing acute about it: they played points after the misstep, and there was no sign Nadal couldn't run.
That said, even considering that, I agree the umpire has no choice - following the book - to have the trainer call it. At this point the trainer in accordance with the umpire made the mistake to call it an official medical time-out. By the way, that alone already took some time; Nadal took off his shoe, etc., tried to explain things (even explaining at what point of the match it happened, which was quite useless info). I'm no trainer so how do I know they made the mistake of appointing it as a legitimate time-out? Because Nadal ran around like a rabbit on duracell right after the time-out. (Also, if I remember correctly, the point at which they pronounced it was a time-out was closer to the tie-break than to the previous game in time. So it's not like Nadal got better thanks to the time-out.)
There is something wrong with the rule too, though, because 1) letting the trainer call the shots (understandably so though!) already implies some form of time-out and 2) again, if this is acute, then everything is acute - because there might always be a possible fracture.