The reason for the above is that thin wires in the first swivels made the thick leader line (100# fluoro) take too sharp a turn, causing the line to break (right were it went around the swivel) at a lower pressure.
The thing you need to know is that if you tie a thick line around a thin piece of terminal tackle, the knot will break at a MUCH lower pressure. That is what got me started on this thread.
It will increase the effective diameter of the swivel wire a bit. It might also reduce chafing between the line and swivel. My inclination would still be to select a swivel with larger diameter wire since that would speed retying and give a more certain result.