Because Sunk Costs can encode information, should Sunk Costs really be ignored?
It's all about the precise idea these authors are trying to communicate:

A) Mankiew is explaining that we are sometimes too stuborn: we sometimes make a bad investment and then feel some vindication in making another bad investment that might rescue the first one, even though we know it's a bad investment on its own. In abstract terms that can be stated by saying that sunk costs should not be taken into account when evaluating whether to increase an investment in a project. Say you put in 100 dollars in a project (A) and got nothing back but you think if you only put in another 100 you will at least get you original 100 back. However, there is another project (B) that pays you 101 if you put in 100. We have the tendency to try to rescue our bad investment and put our money in project A again, but project B pays us a higher return, and we should go for project B.

B) Baliga and Eli are explaining that although, as Mankiew says, you should not use sunk costs in your calculation of whether a new investment is good or bad, it makes sense to keep track of sunk costs from an informational perspective. If you tend to forget what you did or how well it turned out, then recording your sunk costs in a notebook might help you figure out which were good investments previously and might be good in the future too, or not.