If the "ring of death" problem with the 360 is truely due to poor connections made by the BGA's, then the goop should help. The problem is that the electronics industry has moved away from using lead in solder due to environmental concerns. Lead allowed solder joints to be flexible and move when stressed due to board warpage and heat. By removing the lead, the joints have become stronger but more brittle. This is all relatively new to the whole industry (European laws went into effect June of 2006) and has caused a large problem for the industry as a whole. If anyone is interested in this shift, then Google RoHS (restriction of hazardous substances).
The strongest solder joint comes from an OSP finish(organic solder plating, which is bare copper covered with an organic covering to reduce oxidation) on the PCB. The Elite and original 360 motherboards use this type of plating, based on the photos provided on the above listed website. Obviously, this must not be enough. The new thing to do in battling these problems is to "glue" the components to the board as Microsoft has done here. Another option would be to underfill the BGA component, but this makes rework very tough and time consuming since the entire area underneath the BGA is filled with an epoxy.
We have had a few problems with BGA's solder connections breaking recently on the leadfree assemblies. We have had to do a lot of research on feasible cures for this problem. One of our customer's design has gone to a glue remedy similar to Microsoft's to battle broken BGA connections. Their previous fix to get the prototype working was to add a piece of foam to apply constant down pressure on the BGA so that all the joints made a connection. Be glad that wasn't Microsoft's fix!