You are correct that certain food cooked entirely by a non-Jew may not be eaten by a Jew.
Here are a few paragraphs from the Chabad.org Kosher Handbook:
Certain foods which were completely cooked by a non-Jew (bishul akum) may not be eaten, even if the foods are kosher and are cooked in kosher utensils.
Foods that generally come under the category of bishul akum are: 1) Foods that cannot be eaten raw, such as meat or grains. (This excludes foods that can be eaten either cooked or raw, such as apples or carrots.) 2) Foods that are considered important, "fit to set upon a king's table." There are various opinions regarding what are considered "royal foods."
If a Jew has supervised and assisted in the cooking of these foods, such as by lighting the fire of the oven or stirring the food, such food is considered bishul Yisrael and is permitted.
These laws affect many commercially prepared foods. Some supervising services write the words bishul Yisrael on their hechsher (Kosher certification). These laws must also be kept in mind when enlisting the help of a non-Jewish housekeeper or cook."
The key is not so much that a non-Jew may not light the fire as that a Jew must light the fire or otherwise participate in the cooking in a meaningful way in order to render the food kosher.
If a non-Jew cooked the food alone, without Jewish participation, the food as well as the utensils are not kosher and the utensils must be koshered.
Important Note: The above follows the accepted custom of Ashkenazi Jewry relying on the ruling of the Rama who contends that symbolic participation in the cooking process such as lighting or adding to the fire is sufficient to render the food permissible.
On the other hand, Sephardim follow the ruling of the Beit Yosef who maintains that in the case of cooked foods a Jew must actually place the food on the fire.
I hope that I've been helpful today.
Rabbi Menachem Posner