Saying "lethality is the same as M855 at 300 meters" is not saying "M193 fragments at 300 meters" or "M855 fragments at 300 meters." Technically if "lethality," (a variable I have never seen measured quantitatively) was "zero" for both then they would be equal and that statement would be true.
I suppose we could measure lethality like the LD50 used in drug/toxin tests. LS50 might be the "lethal strike in 50% of subjects." Still, I'm way off the track now and I doubt such a variable could accurately be measured.
In short, be skeptical of any description of "lethality." It's almost meaningless.
One other thing to remember about most of the military tests I have seen is that they don't seem to have data on the interim ranges between 100 yard/100 meter marks, e.g. 125 yards, 150 yards. As I pointed out before all the interesting stuff happens under 200 YARDS. After 200 yards both rounds are effectively a .22LR. Penetration with little, if any, yaw. At this point I think the lethality (which I hate talking about anyhow) is pretty much the same, with a slight advantage (if you think more penetration = more lethality) to the M855 because of retained velocity.
My answer to your question is that I don't totally believe either account. I haven't been able to keep velocity of either round much above 2400fps at 200 meters from a 20" barrel much less 200 yards and I don't consider pure penetration to be a metric of lethality in isolation. (A .177 BB penetrates pretty well at 3000fps but doesn't leave much of a wound).
To my way of thinking 5.56 rounds need to fragment at least 20% to do any serious wounding. I don't see this happening below 2600fps. If anyone knows of 5.56 rounds that are still above 2600fps at 300 yards (or even 200) I'd like to know about them.
Even leaving the barrel at 3250fps by 200 yards the M193 round is down to 2580 or so at 1480 feet altitude, 50% humidity, 70 degrees and 29.53 inches of mercury.
The same conditions put the round around 2250fps by 300 yards. I don't consider that all that "lethal."
For lone operator purposes it shouldn't make a difference. Anything over 200 yards should be a escape and evasion exercise.