Wow, lots of misinformation in this thread.
Some people have automatic payments set up for credit cards, so they don't look at each statement. The assumption that just because the bill was paid that the charge was legitimate is not correct. Sometimes corporate cards are paid and the statement looked at later.
In the US, you have 60 days from the time you receive your statement with the charge on it to dispute it, not thirty days. If the charge is made on the first day of a statement cycle, that means it will be a month before it's on a printed statement, and they have another 60 days past that, so it can easily be 90 days to dispute it.
There are countless threads here about travel agencies and airlines wanting to verify credit cards when the person purchasing the ticket is not the person flying. United for example still checks on occasion, there was a thread started a few weeks ago about Travelocity checking, etc. It's really not that uncommon at all.
So yes, you can be asked by the travel agency to have the card holder verify the charge.
There have also been cases where the airline has charged back a travel agent for taking a card transaction like this where it was a fraudulent charge. When the card holder put it in dispute, the airline (US Air) blamed the agent for accepting it.
It's also pretty common for hotels if you are paying for somebody else to be asked to produce the card.