Cannot open office documents on desktop from folder with unique permissions

Question

I had to setup a library with unique permissions so that a group called payroll only had access to the library and not the site:

-I removed payroll from the site permissions.
-I broke the inheritance to the library and added permission to payroll.

When I click on Excel docs, it opens in Excel web services. When I click on the "Open in Excel" button to open Excel on my desktop, it tries to download and open it but can't. It gives the error "Sorry, we couldn't open [file location]". For Word and PPT files, it tries to download the files and open it too but they get the same error. If I give read permissions to payroll at the site level all documents will open fine. Any help would be appreciated. Thank you.

Below are some additional details:

-change permission on payroll from read to full control, however document still won't open
-tested on IE8 and 11.

Answer 1

This had to be a permission issue so, I create a custom permission level and ran some tests.

In this custom permission level I only checked the following under "Site permissions":

1.Use Remote Interfaces - Use SOAP, Web DAV, the Client Object Model or SharePoint Designer interfaces to access the Web site. 2.Open - Allows users to open a Web site, list, or folder in order to access items inside that container.

I set this custom permission level to my desired group. Afterwards, the group could access and open office documents in the folder, however they couldn't browse the site.