No, you cannot do it online.

As mentioned above, if he calls (by phone) and gives the flight number only (i.e. does not actually mention to the agent anything about changing the time), the system will change the pickup time without changing the rate.

He can ask the agent to confirm the rate before the agent saves the change.

Apologies for any confusion--by "only within the same calendar day," I meant that you can only change to earlier or later on the same day (i.e. you cannot change to pick it up the previous day or the next day). You can actually make that change anytime you want, even months in advance. I edited my post above to avoid confusion in the future.