Basically, DOT has said they reserve the right to call anything cabotage, but in general, they have told the airlines they will only enforce obvious cases:
In response, the Enforcement Office emphasizes that the sale or holding out, either explicitly or by course of conduct, of transportation between two points in the United States via an intermediate point or points in a foreign country may be illegal regardless of the duration of the stopover, the passengers immigration status at the intermediate point or points, the number of tickets under which the transportation is conducted, and the number of foreign air carriers under which the transportation is conducted if they are working in concert. However, we are not likely to pursue enforcement action except in straightforward cases, such as those in which the transportation was continuous (including short stopovers that were incidental to or otherwise did not break the continuity of the trip), the transportation was conducted pursuant to a single ticket, the carrier or its agents knowingly sold two tickets covering cabotage service, the carrier or its agents held out cabotage service via the Internet or other advertising media, or the carrier explicitly or tacitly accepted, benefited from, or participated in a substantial arrangement with a third party to conduct cabotage operations.
So basically, the questions to ask are:
1. Were any legs on domestic US carriers? (if yes, it's not cabotage)
2. Was it booked as a single ticket, or was there any attempt to hold forth or sell this as a single ticket? (if no - unlikely to be cabotage)
3. Was there a significant purpose or significant time spent in the foreign country, making it more than an incidental transit point? (if yes - unlikely to be cabotage)
4. Were the carriers or travel agents working in concert to provide service between NYC and GUM? (if no - not cabotage)
So when you have tickets that you booked completely separately on two different carriers, and it was priced as two completely different round trips, and you have legitimate purpose where you have a specific need to be in ICN other than a simple transit, and you spend more than 24 hours in ICN, there is zero chance of it being enforced as cabotage and your travel agent is (probably) stupid.
Under their apparent belief, it would be illegal for a businessman to book a trip ICN-NYC-ICN one week and ICN-SFO-ICN the next, because it would be cabotage between NYC and SFO. They likely got a warning about cabotage related to GUM (there was a recent DOT case filed by an idiot blogger who intentionally booked a real cabotage ticket) and are blowing it all out of proportion. Ask them if GUM was any other city in the US, would they be concerned? No. They would not.
I would appreciate if you could ask the travel agent what prompted her to suddenly be concerned with the concept of cabotage. If there is a warning going out to travel agents, it would have bearing on something else I'm working on, and I would love a PM or e-mail with the details.