I've had the no medal 5k crits happen on fresh targets right at the beginning of a warzone. While this may be true it definitely isn't the only cause of not getting the crit medal and I still haven't been able to narrow it down.
Apologies.. I have 1562 Cunning and 1444 Endurance, 596 power, 100.85% accuracy, 572 Expertise = 11.2%, 24% crit with 64% multiplier. I have BM gloves/helm/implants/ear the rest champion besides Columi chest.
In order to get the big crits, I usually have to pop my Rakata power adrenal for 565 power and my champion relic for 355 more power.