This misunderstanding is a lot more common than you would think, due mainly to the fact that people without experience of bed bugs often get them confused with dust mites which require powerful magnification to be seen.  Because every home has them and they are the first creature people associate with beds the misunderstanding perpetuates.  The reality is that dust mites are not even insects and are incapable of biting people.  The skin reaction actually comes from a localised allergic reaction to their droppings deposited after they have fed on our shed skin cells.