I'm not sure it's a fundamental mistake. To make a counter-argument, if one travels back to some point in time, but can't remember (or don't know[0]) exactly when a major event happened, one might query it, to see if/when it has happened. Or one might query it because one is mistaken about when it happened. In either case, one might expect to see queries about things in advance of their occurrence. So while this particular work certainly doesn't rule out time travel, I don't think it's fundamentally flawed. Perhaps overly optimistic though.
[0] One might presume historical records are somewhat corruptible, and therefore someone from the future might not have perfect knowledge of when major events in the past actually occurred.
The iPhone 42s contains all the worlds knowledge past present and future and you just need to think about what you want to know and it will send it to you telepathically. Why on earth would I use something as archaic as Google search from the 21st century?
Siri is a still humourless cow though.
[0] One might presume historical records are somewhat corruptible, and therefore someone from the future might not have perfect knowledge of when major events in the past actually occurred.