On the bias is on the bias. People tend to get too caught up in rules. Remember the one about how the gal always put a dish of water in the oven with her pie but didn't really know why other than she did it because her Grandma did that? The reason was, Grandma's oven rack was off balance.
So, fabric is either cut "on grain" or "off grain". Yes, the 60% thing is fine, it is STILL cut "on the bias". I do that all the time when I need bias cut fabric.
Further, there are only two distinctions in fabric, on grain or off grain. Doesn't matter whether you cut it LOF or WOF.
Hope that helps.