Hello, Kjellis85,
Looks like you are not setting the "Size threshold" parameter in the "Close Holes" dialog.
The default value of 0 means that PhotoScan will try to close all holes, regardless of their sizes. That also includes the outer boundary of the surface region, so the duplicate surface is created. This results in unpleasing effect and is obviously not desired in your case.
Please try to specify a non-zero value for the "Size threshold" parameter to limit the size of holes to be filled. It is measured in a number of edges that form a hole boundary. Try some value around 100, increasing it further if required.
With best regards,
Dmitry Semyonov
AgiSoft LLC