Symptoms
The client had difficulties creating a SharePoint 2013 integrated process using K2Studio. Even though the SP2013 site was valid, the client saw the following error when trying to create a SharePoint integrated process: The site does not exist or no connection can be made to the site. Specify a valid site.
Diagnoses
The client was using the "SharePoint" K2 Template. That template is used for integrating with SP2007 and SP2010 sites.
Resolution
I showed the client how to build a SP2013 integrated process using K2Studio. We created a "blank process" and dragged the SP2013 process wizard onto the canvas. From there, the client was able to build a SP2013 integrated process.
Additional Information: I routed the ticket to the LABS support team so that they can log an item that will update the K2 Template descriptions. (It is a little confusing.)