The Household Production Function
I have only read the abstracts, but the two statements aren't conflicting.

From Wikipedia, a production function gives the technological relation between quantities of physical inputs and quantities of output of goods. A household production function is a form of that idea that looks out how households combine inputs to get outputs that they consume such as water. 

Under the HPF model, water is considered as an output that households consume. However, there are many ways to combine inputs to obtain water: you can use utility based water if the infrastructure for that exists or non-utility based water (involving personal tanks, pumps, etc). The assumption is that households will be willing to pay for the utility based water infrastructure at least the amount that it takes to upkeep their non-utility based water that they currently own accounting for the sunk costs of the upfront purchase of the tanks and pumps. And hence that is the "lower bound to WTP". But this assumes that the utility based water is higher quality than what households already have. As noted in the abstract of the latter paper, "[w]e attribute this departure from the traditional relationship between averting expenditures and contingent valuation to the lack of household confidence in the quality of utility-provided water." Hence, current coping costs become an upper bound to WTP. To put it differently, if households believed utility based water is exactly equivalent to what they currently have, then the WTP would be exactly equal to current coping costs.