The component clearances are verified/checked based upon the 3D-Body information embedded in the footprint of the components. I'm going to guess that your footprints are either missing their 3D bodies, or the 3D bodies do not accurately represent the component or your intended mounting style of said component. For instance, the 3D body of the display component may be drawn with the display flush against the board surface, versus raised off of the board to accommodate components placed underneath the display. You would need to create a new display footprint with the appropriate raised 3D body in this case. Once you have the correct 3D body information in place, the acceptable component clearance is defined in the Design Rules, under the
Placement > Component Clearance rule set.
Note that in the case where the 3D body information is missing from the footprint, the component's size is defined as the smallest rectangle that contains all of the primitives on the silk and copper layers (excluding the designator). The height is defined by the height value specified in the component properties. This method is very limited and will not accommodate cases with vertically overlapping components, so I suggest creating 3D bodies for proper clearance checks in this case.
In the layout tool, you can press "3" on the keyboard to view the PCB in 3D mode and review the 3D bodies of the components currently on the board. You should be able to see which parts require changes to their 3D bodies, or if any components are missing them completely. (Press "2" to return to 2D view.)
If you need to modify/create a 3D body, you can reference the following Altium tech doc...
http://techdocs.altium.com/display/ADRR/PCB_Obj-3DBody((3D+Body))_ADGood luck. Let me know if you need any further clarification.