In short, if we think some information will be on the internet later, we are likely to not bother remembering that information today.
One way to interpret the results of the study is that, where we have a chance to jettison information, we do. Hopefully, “jettison” means to “compress” information into a handy rule of thumb, word, concept or theory which we reuse with efficiency, rather than to reuse the original data set over and over again in all its unwieldy bulk. Sometimes however, we can be conned into simply erasing or otherwise strongly de-prioritizing memories without bothering to create a useful summary of what we’ve lost. This supports that idea that our memory erasure mechanisms (or de-prioritization) are separate from our symbol creation mechanisms. This would make sense from an incremental, evolutionary perspective. It would also suggest that I should not assume my “transaction model” of cognition represents the working of a single mechanism.
It is interesting that one of the researchers (Wegner) refers to this as “transactive memory” (this might be related to transactional analysis in psychology).