I think there are a lot of variables here that impact whether or not it's a good business decision. To start:
1) How many providers are you credentialing?
2) How often do they come and go?
3) How responsive is the credentialing service you hire?
4) What are their fees?
5) How much time do you currently spend on credentialing and does that impact delaying other work you deem more important?
6) What are your current credentialing obstacles and would outsourcing even alleviate those obstacles?
For example, in a small office with steady providers, I don't think an outside service is worth it. If you are a larger group, or frequent provider changes, then I would debate between in house dedicated staff and an outside company.
It's the same type of decision as using an outside vs in house billing. There is no one right answer.
I worked for a small practice as biller, then billing manager, then office manager; I handled all credentialing myself from day 1. I only had issues when I first started the job and a prior employee had not properly updated an address and bank change with all carriers. Over the years, I added a PA, replaced that PA twice and added an MD, all without any financial hiccups.
We then joined a very large healthcare organization that uses an outside company. However, the system seems so convoluted that my organization has several in house employees just to communicate with this outside organization. When we joined them, it took almost 6 months for the insurances to have our updated TID/group and was a huge financial mess. Claims were being denied as out of network. New payments were going to the old group. Old payments were going to the new group. New payments were going to the new group, but not allocated to our providers.
Just like with an outside billing company, you are giving up some level of control when these are not your employees. Any mistake can have significant financial impact. If this outside company are experts, they may make fewer errors than you would. If this outside company doesn't pay attention to details, they may make more errors than you would.
My guess is the only statistics you will find will be from the credentialing companies themselves trying to sell their services which I suspect could be biased toward the benefits only.