PCBgogo

Hi,
We are having some failures on a run of our product. I've spend the last two day's trying to figure out what is going on, and it basically came down to the PCB factory blaming the oven profile used, and the Assembly house blaming the PCB and paste stencil tolerance.
I'm in no way an expert in these kind of things, and I would like to get a 3rd party opinion from someone here, that obviously have no special interest in the outcome. Below follows the details and photos that I have collected thus far.
I've asked the PCB manufacturer to measure a panel for me and make sure that the PCB is within tolerance. 
Maximum Deviation: 0.084
Minimum Deviation: 0.002
Average Deviation: 0.0445
I have the full report if more info on this will help. It seems like the maximum and minimum tolerance that they will allow is 0.100 and -0.100
To this degree the stencil was also checked and made sure that it was cut to specification. The Assembly house told me that they did do a 10% aperture reduction. But did not do the aperture reduction on the BGA. But they insist that the panel deviation is the cause of the failure of the boards. Because the paste does not align perfectly with the pad. Attached is photos showing the BGA. There are 3 boards per panel. 1 is left. 2 middle, and 3 right.
Some details about the BGA:
Pad Diameter: 0.3
Ball Pitch: 0.8
Ball Diameter: 0.3
Ball Count: 324
Symptom of the Failure is basically some board will not work, unless I press down on the BGA, and some features (like USB) not working. I have had quite a bit of success working with the repair technician in getting the boards working again by reflowing the CPU.
We took x-rays of the BGA as well. The x-ray technician said that everything looked  good and aligned to him. But yet the CPU does not seem to start without pressure. I read up a bit and it might be due to "brittle solder"? I'm still awaiting the x-ray images.

So if anyone can shed some light on this for me. I would greatly appreciate it. Is the tolerance of the PCB to low? Does the amount of past look like it will be enough. Is the paste positioned correctly. Any other questions I need to ask the manufacturer's?