Modern Western man had no trouble with these verses. The ancient world would have a much more difficult time. At the heart of the verses is a promise made and a promise broken. For Western man, this causes no alarm, and is rather to be expected since the promise was not affirmed by a phalanx of lawyers. However, in the ancient world, the promise should have had more value. Had there been only ephemeral value in a promise, Alma would not have believed it in the first place. Had honor been of so little value, Alma would have sent this Lamanite army in the wrong direction, for spite.
None of these things occurred. What happened is that Mormon describes a promise made and a promise broken.
Perhaps Mormon misunderstood some of the transaction between the leader of the Lamanite army and Alma "and his brethren" (one of whom would surely have been Helam). Perhaps Joseph Smith mistook the complexity of the situation, and translated this as a promise broken, when the actual "promise" might have been quite different. Note that what is promised is "liberty." While we have our own ideas of what that means, the Mesoamerican definition may have been different than what we imagine. Limhi's people maintained their city, their ability to trade, but were nevertheless required to pay tribute. The Almaites are allowed to live, and perhaps that is a possible definition of "liberty." In the context of the following verses, it would appear that the Lamanites were setting up a tribute-paying dependent, just as they had done with Lehi-Nephi. What the Lamanites do is set up guards around the city, just as they had done with Lehi-Nephi. This suggests that this was a fairly parallel occurrence, a fairly standard practice for a people that had been subjugated.
The translation of the verses appears to describe treachery, and perhaps there was some misunderstanding on the part of Alma's people, but the nature of the Lamanite actions suggests that they were merely following a standard protocol for a "conquered" people.