Most likely the words that you quote mean that no. When you look at the deformed shape of the transverse section of the loaded through bridge the top chord will get induced deflection and this with transient load; hence it seems AASHTO has seen good to limit the deformation as well through this qualitative clause mandating or expressly recomending that the bracing members be deep.
This must mean that such detail by whatever the reason (overload, impact, limit capacity) has been of superior behaviour. For, in one aspect, it needs not necessarily be, for deeper members have less rotational capacity for the same flange welds (you need to have more rotational distortion in the less deep member to get a Fy stress at flanges), and, depending on the detail, a capable design could show superior performance in fatigue with a less deep brace. Yet anyway a deeper member also restricts the intervening rotation, and it seems the experience at AASHTO is that deeper braces perform better.