Use of remote control products such as Webex Remote and GoToAssist

I would like opinions on the use of Webex Remote and GoToAssist as tools for providing remote support to a companys systems and servers from anywhere in the world rendered by its own internal support staff. It seems to me it would be far better to allow connectivity to a network from the outside through a centralized controlled mechanism such ISPEC VPN or an SSL solution. Each connection would then be centrally logged. After the remote system connects to the internal network and passes a policy check, remote support sessions could then be allowed to the corporate systems requiring support by using approved remote control software. I would also prefer these external VPN or SSL sessions be initiated from corporately owned systems (located outside the network) conforming to an approved security policy rather than from an unmonitored personal PC. It seems to me that by allowing GoToAssist and Webex Remote sessions from anywhere in the world to any system inside a network you are assuming increased risk and increasing the possibility for unauthorized access. Both Webex Remote and GoToAssist have their place for occasional support use or for supervised vendor support sessions, but I'm really concern about allowing increased usage of these support tools just to accommodate ease of use when we in turn assume increase risk by using them. I would like to hear opinions on this topic. I may be wrong and the experts can be put me at ease.  Thanks ahead of time for the input.