You can autoclave anything. It is just a big steam sterilizer. They are used for instruments, supplies, culture media, anything you need to be sterile. There is a solids cycle for instruments and a liquids cycle for culture media (so it doesn't boil away). You can sterilize infectious waste before disposal, but I doubt anyone would try this with a body. This was during the day, and these are usually in an equipment room where anyone could walk in at any time. There would be no reason to do this- it would increase the chance of discovery immensely.
Anyone who needed to use it could learn how to use it. Sometimes in a large lab there is a technician responsible for all autoclaving.
In over 20 years of working in labs I have never seen an incinerator inside a lab. Not that it's impossible, I just think it's extremely unlikely.