I think your question is relying on two completely different definitions of "high" EDTA. Really, both concentrations are "high" but one of them is "really really high."
The only references (for example, here or here) I can see that say anything about osmotic effects of EDTA is in the context of blood sample collection, and specifically when too small a volume is drawn into a larger tube, for example 0.5mL blood in a 5mL tube. In this circumstance, a ~liquid (blood) is added to solid EDTA powder sitting in the tube. This is already a high concentration of EDTA, it's enough to mop up all of the calcium around to prevent coagulation.
However, if you only fill the tube 10% full, there is 10X more EDTA powder pre volume than necessary to prevent clotting. This isn't just high, it's incredibly high. EDTA is usually as a potassium salt in this context, so that could be as much as ~100mOsm which would definitely cause osmotic effects, but that's on the order of a 10-fold higher concentration than your reference for platelets (which I can't access unfortunately). When you state in your question:
I know that high concentration of EDTA increases plasma osmolarity which leads to cell shrinkage
...this seems to be the best explanation, unless you can show another reference that demonstrates substantial cell shrinkage at lower (~2mg/ml) concentrations. I'm not saying there can't be some osmotic effect at that level, just that it would only be a couple percent of cell volume and would not be noticeable on anything but the finest assays.
Then on the other side of the equation, the effects on platelets are not to do with osmotic effects but rather due to a somewhat paradoxical activation of platelets, as in @DavideN's answer. Think of platelets as cells that are "primed" to expand when needed to stop a bleed; in some circumstances, it seems like EDTA can be a trigger for this process to occur, though not in others (again, see @DavideN's conflicting references).
Goossens, W., DUPPEN, V., & Verwilghen, R. L. (1991). K2‐or K3‐EDTA: the anticoagulant of choice in routine haematology?. International Journal of Laboratory Hematology, 13(3), 291-295.