In your example, that middle-person verifies that what you are purporting to sell, TSLA stock, is in fact TSLA stock. They provide value by way of quality assurance and recourse if fraud is involved.

How can I be sure what you're selling me is in fact what you say it is? And if it's not, what recourse do I have?

If I buy something directly from another person on Facebook Marketplace or Craigslist, I'm not going to pay full retail price, even if the item is unused, because I'm giving up any form of recourse if the item is defective that I would have received had I purchased directly from the manufacturer.