Algos is this something you actually know or are you speculating? Is it compensation in exchange for referrals if the doctor is an employee? A percentage of collections would simply be how the employee is paid. Lots of employees work on commission without it being considered a kickback, and it's certainly not "ownership".
As for the % number sought in the root post, people love "50-50" deals. They think it's "fair". I would start with 60% and see if they will counter-offer 50%. In exchange for them doing everything and paying for everything 40-45% wouldn't be all that bad. Make sure it's gross and not net.
You will need to spell out a lot of terms and conditions because you are forfeiting control over a lot of things that you control absolutely when self-employed. Suppose you feel you need a piece of equipment or you want nicer furniture. Who decides whether or not you get it, and what are the rules?
Who pays for malpractice, meetings, books, computers, and so on? Will they pay for your car? How about gas, parking, etc? If you're self-employed those are potential business expenses. Buying with pre-tax dollars through your business is a powerful thing.
Who has the final say on hiring and firing of staff? Suppose you hate the nurse but they won't replace her?
If you're truly an employee you are eligible for any health insurance, 401(k), etc, they offer. What are those like, especially the 401(k) - how many years to vesting? Matching contributions? What kind of investments? Some employers screw the employees by getting a plan with low management fees in exchange for only offering investment vehicles that provide front-end commissions to the plan manager.
Finally, consider that you will probably hate working for the hospital unless you enjoy being treated like chattel. I can't imagine having a hospital administrator sign my paychecks. As I mentioned in another post, it's probably the way medicine is headed for a lot of doctors in the future, but I would have to be dragged kicking and screaming.
Would they consider a first year income guarantee, reduced rent on one of their offices for one year, and you set up your own practice? It's legal and that's how I'd do it. You could walk away from it a year later, set up an office down the street, take all your cases to the competition, and there's not a damn thing they could do about it - because they can't offer compensation and demand referrals in exchange.