Our two gas turbine experts have explained to us that the pressures in the various chambers are such that the forces on the shafts tend to cancel and there is very little nett load on the bearings.
If I understood correctly, they explained that the pressure forces are significant, and hence have a tangible effect on bearing axial loads. This is not the same as saying the bearing loads are very little.
The design aim will always be to minimise bearing axial loads as much as possible, as simpistically they then last longer - which is a good thing.
However, as explained in the CF6 link from the manufacturer, the axial thrust fan bearing load is still nearly 20,000lbs. This is not "very little", when compared to a total engine thrust of around 50,000lbs, though it is lower than the oft quoted thrust force that is created by the fan (i.e. 80% of the 50,000lbs). It would be interesting to know whether later gen engines have actually reduced these axial loads further through careful design of turbine section - as the CF6 data is quite old.
Is any of the bearing axial load discussion relevant to these failures - personally I suspect not, but it is quite an interesting aspect of the engine design.