I'm no Engineer, and not the smartest tool in the oven, but.... If you think about the trailer and it's weight, it is is designed to actually sit on the axle mounting bracket. So, unless your getting airborn in your Airstream, securing it to the frame does two things; 1) keeps the geometry of the suspension in the torsion arm and/or shocks (if you have them) in line, and 2) keeps the axles attached to the trailer, also again, in line.. There are two types of strengths to consider, shear and tension. Tension pulls in a straight line, with say, the bolt, and shear pulls perpendicular to the bolt. Shear is stronger, and that is why they are mounted through the side of the frame rail. That puts the bolts in shear vs tension. Plus it makes it easier to access, if you need to replace them...
Hope that helps..
p.s. no comments from the peanut galleries, I disclosed I am NO Guiness... :-) CHEERS!