For clarification: not ridiculous. Incorrect for his application, but not incorrect in general. There are more than a few factory setups with the cat behind the muffler. Don't ask me why; I don't know. But it exists, and I've seen it. A GMT400 example: my 1995 3500HD had stock exhaust and the muffler is ahead of the cat. This is also on a manual-trans equipped truck with a one-wire (non-heated) O2 sensor. Of course, emissions standards are more lax on higher GVWR vehicles, at least back then, so go figure.*
Back to OP's truck, cat comes before the muffler in THAT application. Your stock exhaust (some of which sounds like it's still intact) is each manifold connects to a Y-pipe, Y-pipe has a cat bolted to it at a flange, and the muffler is behind the cat.
* Sidebar interesting story; a 3500HD although being 15,000 lb GVWR is listed on the title as "1 ton" so they tested it against 1 ton standards - 10,000 lb GVWR shown on the test sheet. It passed beautifully, especially for a 281K mile TBI 454 with what appeared to be the original cat on it.
Richard