I only have 3 AG batches under my belt, but the most valuable lesson I learned about strike temp was during the first batch. I was WAAAYYYY under, at only 140F initial mash temp despite trying to preheat the tun.
The MLT cooler will suck up a lot of heat, as will the grain. Beersmith is probably assuming you're preheating your MLT and won't lose any more heat to it, and is only factoring in the heat lost to the grain at room temp.
I found the best method for me is to add most of the strike water to the MLT at about 185F, and let the temperature stabilize (at least 10 min or so). I measure the temp of the water, trying to hit the temp that Beersmith says for a non-preheated mash tun (in your case it sounds like that's the 168F). Then based on whether I need to get the temp higher or lower, I add more water to get to what I want the volume of strike water to be and at what temperature I want the strike water to be. THEN once the temperature and volume are stabilized at the strike specs in the MLT, I add the grain slowly and stirring to keep doughballs from forming.
Using that method (add grain to strike water) I hit my mash temp on my 2nd and 3rd batches dead-on.