If the users's time was 1970-01-01 and they were shown a page titled "tomorrows reservations", it would show no reservations.
However, this would be correct from the user's computer's perspective, just not from reality (unless maybe they are traveling at light speed).
In my opinion, despite the advantage of always showing reality, no matter what time the user has, it's better to use the client's local time for the following reasons:
- expectations
- accuracy