Lakland's Joe Osborn set comes (or at lest used to, it's been years since I bought a set) a warning not to string them through the body. However, I've got a set on my Sting bass and there's not been any problem. It seems that the reason for the warnings is that it MIGHT cause the string winding to break, and the warning serves to clear the string company from obligation under any warranty.
So, if you choose to string any specific set of flats through the body, and they warn against it just know it's at your own risk. BTW, if youi have a choice between top-load and STB, go with top-load for flats. My experience is that all the advantages and indeed, differences, of STB are in the head. I strung my Laklands with the E and D through the top and the A and G through the bridge. I couldn't hear nor feel any difference in a true side-by-side comparison. When I restrung that bass, I alternated so the E and D were STB and the A and G top-load. No difference at all. So, for flats, just to be safe, I'd go top-load if it's an option.
John