Have never heard of routine autoclaving/sterlizing of linens
Operating room and other linen that *must* be sterile; yes, that is another matter.
Back in the day when hospital stays were for several days or even weeks, and nearly everyone got a bath and change of linen every morning, followed by changes required due to soiling during the day, floors and units generated huge amounts of soiled linen. Laundering alone was a huge enough process, it would be very costly and time consuming to also autoclave all those sheets, pillow slips, draw sheets, etc.
Thing to remember as happened in both the linked OP and my own links is that persons who succumbed to infections were already immunocompromised. In that weakened state any bacteria, virus or fungal infection could take hold and prove fatal. That and of course the very young (newborns, children), and perhaps the elderly. This falls into what every nursing, medical and other healthcare professional learns as a student; for the most part germs or whatever on surfaces aren't going to cause illness. The human skin and other systems are remarkable in their ability to keep germs out and or deal with them before they get too far into the body. Again this is for healthy individuals with good immune systems. Long as key hygiene is remembered (washing of one's hands, not putting fingers in mouth or touching eyes, etc...), most all of use are pretty safe.
Think about it; were things otherwise humans would have largely vanished off the face of the earth from disease. Say this because there are germs, including some very nasty ones all over every single surface we come into contact with daily. If you could see what is growing on your keyboard, telephone, that pole you hang onto while riding the bus, your car's steering wheel, heck even your own loved one's hands, you'd never feel safe in your own skin again. You'd certainly not let anyone touch you!
Problem with fungi is they are everywhere; their spores are airborne and that casing makes them difficult to destroy.
This feeds into the debate we've long had here and consumer groups have taken up regarding the merits of various "sanitize" cycles on dishwashers or "boil washing" cycles on washing machines. Sure when things come out they *might* be very well sanitized or even near sterile, but soon as fresh air hits them a new crop of germs and fungi will settle down. If you dry your laundry outdoors in the "fresh" air, well there you are then.
Just as you cover foods when out in open air, so should clean linen. In my day linen was never left uncovered during transport. We were taught in school *not* to carry linen against our uniforms. You didn't shake or unnecessarily fluff linens in the air when changing soiled linens, nor making a bed with fresh ones either.
The problem these places seem to be having is they've outsourced their laundry, but no one is taking the time to assure quality control. In the case that Louisiana children's hospital the so called "infection control" nurse didn't even bother about newly delivered clean linen being left uncovered on loading docks.
In a modern high tech laundry there are plenty of chances for laundry to become "contaminated".