Unable to create or migrate site collections to SharePoint 2013 (4222785)

When creating or migrating a site collection to SharePoint 2013, you receive the following error message:

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This case is isolated to SharePoint 2013 connections via the Extensions Web Service (MEWS). Furthermore, the connection is a "Web App" connection type. This is not an issue when using the "Farm" connection type to SharePoint 2013 through the Central Administration URL.

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Because the connection is going through IIS, there is a need to use the application pool identity for escalated privileges. This necessity is due to the Claims Authentication being used on the SharePoint Web Applications, whereas the Central Administration site uses Windows Authentication.

1. Add the application pool identity to the SharePoint 2013 farm administrators group.
2. Perform an IISRESET on the WFE servers of the farm.