SYMPTOM:
Consider that a user has been given 'Denied All' Access Control List (ACL) for a project through Project Configuration > Security in Strategy Developer, as shown:

Consider that the same user has been granted access to the project through Web Reporter privileges, as shown:

This user is able to run any reports or documents within the project through Strategy Web.
Now consider this user is granted access to the project through Desktop Analyst privileges as shown:

When this user attempts to execute a report in the project through Strategy Developer, the following message comes up:

Sample Code/Error
The user does not have Read access to this Project object (ID is 'xxxxxx').
CAUSE:
This is a known issue with Strategy Desktop. The issue is not in Strategy Web, because the problem is coming from the fact that ACLs on a project object are not used to determine if the user has access to the project or not. This is determined if a security role is granted to the specific user for the required project.
ACTION:
Contact Strategy Technical Support for an update on the status of this issue.