No matter what side they're embedded with, reporters (should) operate on the premise that reporting what they can, typically after the fact, will improve citizens' understanding of the war on both sides, leading to better decisions by the electorate in the future deciding on candidates based on their stated foreign policy goals.*
Reporters violating off-the-record or classified-info agreements torpedo that entire concept by ensuring reporters are only given access to purely one-sided, on-the-record sales pitches. It doesn't matter which side reporters want to embed themselves with. If they violate their agreements then their access is revoked, which is worse (long-term) for everyone.
Furthermore, a reporter embedded with enemy forces has to expect frequent disinformation, both on- and off-the-record, but particularly off-the-record if the enemy is the least bit competent. If a reporter reports such stuff, the enemy wins twice, first by potentially getting U.S. forces to prepare for a non-existent attack, and second by revealing U.S. reporters as spies rather than merely unwitting dupes.
*Obviously, big media are not interested in long-term education of the electorate; they're interested in ratings first, and driving their backers' foreign policy agendas second. The net effect is the same, however, since without continuing access (which is contingent on abiding by agreements), the media loses ratings and the ability to twist "news" into supporting a predetermined foreign policy view. Then they have to find something other than the war to report on.