I agree overall but it also depends. In this economic climate with layoffs common backstabbing is not the worst short term strategy. OP would essentially be using their accumulated political capitol to make it more likely that their manager gets the ax versus them.

The skip is most likely doing a calculation of how much OP is worth versus how much the Manager is worth to the organization. Showing too much respect means the calculation is less likely to go in OP's favor since even OP seems to see Manager in a mostly positive light.