This started as a comment.
It's important to point out the "Who's at fault question". If you use a third party service and they fail to provide it's their failure to provide. If you use something in house and it fails, now it's the house's fault. Such distinctions carry a lot of weight. It might not mean anything to actual security, but that can sometimes go to the sidelines.
For example if you need to gain certification for a contract, and that certification says something to the effect of:
You must use secure remote management methods, unencrypted remote management methods are not allowed. Contracting with a third party to provide services is allowed. Encryption must be foo strength and bar requirements. Common services that meet theses requirements are LogMeIn and TeamViewer. Common services that do not meet these requirements are GoToMyPC and plain VNC.
Then the decision could be made to use Team Viewer.
Then there is the risk to the business. It could be argued that Teamviewer is less risk, because your using a service in good faith that is supposed to be secure. At the same time RDP may be more of a risk because now your standing your team's knowledge up against random peoples understanding.
In the end, while this doesn't have any real connection to real security, it's important to remember that companies don't do security cause it makes them money (normally). They do it as Risk mitigation and because they have to to keep making money. Using a third party service may remove some of the risk for the company.