You are correct about the wide swath.  Here's an article that may help clear things up.

This article talks about conditioning the stem.  There is a guy in New York who promotes "Hay in a Day" (actually haylage).  His theory/ teaching is that using conditioning rolls actually breaks the stem and slows the drying process.  He says that mowing - no conditioning - and laying in a wide swath is actually the best.  I think he also advocates tedding  a couple of hours after mowing. 

The most important part is to mow and lay it wide, and get it to wilt quickly.