The reliability of a dent is a function of the size of the dent, particularly the width and sharpness of any crease. Sharp creases significantly increase the probability of failure. It won't asplode but it may buckle under loads that normally wouldn't affect it. Of course, the thinner the tubing, the more susceptible it is. Frame blocks are a popular shop tool for removing dents because they reduce the size of the dents and crease, reducing the probability of failure, though at the expense of the paint finish.
As an extreme but easily demonstrable example of how a dent impacts the structural strength of a tube, get an undamaged aluminum soda pop can. Try to buckle it by pushing inwards on the ends. Or try bending it. It's not easy to do. However, if you use your thumb to put a small dent with a crease into the side of the can, the loads required to buckle the can drop significantly. Dents have the same effect on a bicycle tube. However, it's very hard to predict the new, reduced load limit. Moderate dents may be fine for everyday use but could cause the tube to buckle under a bigger impact, such as hitting a curb or pothole. It's impossible to predict.