I feel like I'm logging into this account more than my main! Once again, licensed PE/SE working for one of the big PEMB manufacturers. I figured I'd help try to give some light on how the purlins were likely designed.
The fly brace is how the load is going to get up into the purlins. As mentioned, it's much stiffer than trying to pass it from the bottom flange of the column up to the purlin sitting on top of the rafter. It's one of those things that's missed a lot, but for tall enough buildings, or those with enough wall trib, I will upgrade size/bolts of those connections to ensure it can adequately transfer the load into the purlin.
The purlin itself is (or at least, should be) designed for the extra axial load. By analysis, it's likely that wasn't too much, or else an additional compression strut member (likely cold formed material) would be supplied to help transfer the load into the bracing truss system that I assume is located outside the picture.
I'm guessing the roof deck is a through-fastened system; as everyone mentioned there's no discrete bracing to the purlin bottom flanges. AISI S100 sets the capacity of the section with an unbraced compression flange (uplift) as a percentage of the capacity of loading in the other direction (gravity), based on depth and profile of the shape. This is checked with combined loading from axial, and the gage of the purlins along the strut lines may be increased, depending on how far the load needs to strut to the roof bracing.