The original hypothetical was to create a simulated agent that merely fails to notice a gap. New information does not need to be added for this; information from around the gap merely needs to be averaged out to create what appears to be not-a-gap (much as human sight doesn't have a visible hole in the blind spot).

Now, if the intent was to cover the gap with something specific, then your argument would apply. If, however, the intent is to simply cover up the gap with the most easily calculated non-gap data, then it becomes possible to do so. (Note that it may still remain possible, in such circumstances, to discover the gap indirectly).