If you do a calculation of the number of Ebay purchases that are handled by PayPal, it's certainly in the millions, and probably hundreds of millions. The rate of outright fraud is unfortunately very high, and the average person is so prone to error that PayPal must employ many people to handle all the cases.
Once you have a very large organisation, consisting of many staff handling cases, all of whom need to be acting consistently, you face the real statistical likelihood of fraud within the company itself. Any sufficiently large company will have employees that try to defraud it.
The upshot of this is that large companies handling many transactions like this, especially ones that will often be disputed, must implement security not just to prevent fraud from outside the company, but also inside.
Such security measures are often very difficult to work around by employees trying to do the right thing by customers who are in the right, but where something unusual has happened that those security systems didn't anticipate. I can imagine this often frustrates the intention to have a smoothly working system.
You also can't easily make changes to accommodate such corner cases without opening other security holes, both within and without the company. And it takes a long time to formulate and disseminate new protocols that your employees should work to. And then you have to communicate any changes in the way you handle things to your customers.
Running a company like this must be an absolute nightmare of logistics. And it is surely made worse in that Ebay seems to have the ability to authorise chargebacks and refunds in disputed cases that can then be appealed to PayPal itself.
But the alternative is in my opinion worse. As a buyer, you must pay for an item before receiving it. I am aware of so many complaints online of fraudulent sellers making off with tens of thousands from fraudulent sales, and there being nothing anyone can do about it because of banking privacy laws. Having a service like PayPal seems essential to reducing fraud in such online transactions.
In summary, I can perfectly understand PayPal wanting to perform a security check for every long time customer for whom a flag was raised by some security protocol.
And naturally, there are going to be many false positives, and many unfair decisions taken at such scale.
Independent arbitration would indeed seem like a good idea. But who is going to pay for independent arbitration for potentially millions of disputed transactions? The reality is, almost every single transaction that has already been appealed to PayPal that can be appealed easily to an independent arbiter, will be. So you simply double the (already high) cost of such a service.