I don't think you cheated at all. You modified your plans to find an area where your particular gear load and the camping conditions could be reconciled. To think you cheated is to slide over into the "is fire ever ethical?" discussion - in the situation you described, it's clearly not a violation of LNT, since the land managers set up an area to "sacrifice" by concentrating the non-LNT use.

My original discussion was oriented toward "what do you do when two competing philosophies are apparently at odds?" Using fire, instead of carrying a stove, would be in line with going light at all costs. However, assume that you're not in a dedicated camping area with a fire ring, and that LNT would indicate that it would be best practice not to use a fire. What do you do: go for the lightest load and use a fire, or give precedence to LNT and take a stove? Which philosophy wins?