Under the Accord Framework and Basel II ( I think) the capital adequacy requirements on the four major banks are quite stringent, using a two tier capital. If there was a run on house lending defaults it would impact Tier 2 which in turn would impact Tier 1 as a result of the risk weighting and other criteria. If there was a sharemarket crash or some other run on the shares resulting in a material equity drop in the banks then it would impact Tier 1 Capital and consequently Tier 2 capital or credit lending or existing marginal loans would be possibly called up causing an impact the other way.
The four major banks (CBA, WBC, ANZ, NAB) are termed the four pillars for good reason and they have a capital burden imposed on them which the other banking institutions don't carry as much as it frustrates some people within those banks it helped during the credit crisis and subsequent GFC and APRA will still ensure the comply.
Having your money tied up in one of the four majors is safer than one of the other financial institutions in an economic environment of uncertainly but in good times it will be sold to you as "its good for the relationship" but when things turn really sour, like war, then gold is probably the safest bed.
