I'm pretty sure that the answer is no and they they lose their equipment. The version highlighted says "refer to the main rulebook", which says that dead fighters lose their equipment and it isn't recovered. That's generally true of all the ways to die, and is pretty consistently adhered to. I understand where you're coming from, and it doesn't help that the Mordheim books are notoriously poorly written, but in most circles players tend to obey the idea that "the Main Rulebook is right".

Tbh I think this is one of those that needs to be house ruled on how it plays out at the start of the campaign. For example on the seriously injuries chart in the Main Rulebook, you can roll a result of Robbed where you lose your equipment or the death result as you mentioned.

I think it's saying that, as long as they don't die or some other result that would force them to lose their equipment, the pits return the equipment with the hero