Yes, there are companies which provide an escrow service. Owners mostly will NOT agree to use and definitely Owners will NOT agree to pay for the service. Why?
Owners MFs were paid way before the checkin date. The rental rate is established at the time of "meeting of the minds" and both sides agree. The owner is NOT corporation like Marriott or Wyndham or Sheraton with vast marketing and market presence. It is ME or YOU or your neighbor with an extra week or two. Most owners live several states away from their timeshares as they use them to getaway and to vacation in different weather, etc.
There is a professional onsite group to act as caretaker and service providers ... but not as a collection agent. Faucets drip, refrigerator is warm, key is lost ... yes, those are issues for the onsite management company. If the owner provides the permission for YOU to use their ownership ... they should welcome and treat you (the guest) in a similar ways for those benefits a "Guest" is authorized by the HOA board... at some resorts, the actual owners do get some minor perks (free internet or parking, unit requests) ... guests of owners, renters by the resort management company, exchange guests MIGHT be treated a little different .. no free breakfast, no late checkout, etc. But at my resorts YOU will not be given the WORST room in the house ... unless it was MY TURN to get stuck there. And even I mostly would NOT know til checkin day.
If you are worried that you are paying for an unit which does NOT EXIST ... TUG has a sticky suggestion on ways to confirm the owner DOES own or has a reservation they can rent.
Yes, I rent some weeks out. I print off reservation confirmations from the computer system. I have copies of my deed and/or MF invoices for individual weeks. But what many people learn is "I know my resorts" and if they have been there before, they realize that I have been there a LOT.
But I could also say why should I trust a NEW guest? Paypal charge back, bad checks, rude guests (and yes, I get requests from the resort to NOT rent to THEM again!), and calls at 3AM ... I KNOW that happens at least 3-5+ times a year. And I get calls for airport closed by home & stuck in FL, too. Dang ... I got on the last plane out of FLL one Thanksgiving weekend - hurricane inbound. Resort shutdown; guests told to find other shelter (and not a resort person around ... big name starting with M). Been there ... not fun.
So, if either the owner or renter gets "funny vibes" ... why rent from them? You think "funny" is going to improve if there is an ISSUE? And no season is flawless or perfect ... it is in how you handle the issues as they rain down on you.... hundreds of miles away with strangers trying to work together.