That is quite the wide strap, I never noticed it either. Maybe because it is white against Randy's dark shirt. I've always assumed that the heft and length of the bass is why Timothy perches as he does on the stool with his right leg out, he just can't hold it across his lap like the others can hold their guitars.
Hmm...that strap might look bigger being white...
I have a nice leather strap for mine (Elliott), don't think it's quite that wide...but my Peavey Fury is considerably lighter than that Fender...