I've done oodles of research on hamartomas since my U/S last week. That is the first time I've heard of it being called "not a true tumour". (I like that definition MUCH better 
)
Basically, what I have found is it can occur most anywhere in the body and is made up of the same tissues etc that make up the organ it is growing in/on. I have read in many places that when found in the breast it is often refered to as a "breast within a breast".
I was initally very concerned that a biposy was not recommended unless there were changes. After reading hours upon hours of everything I could find, I've come to accept that hamartomas are easily identified with U/S. From my understanding cancer does not contain fat (even though it can, on occasion, trap fat). I have read that an ultrasound picture of a hamartoma can be compared to a piece of salami. You can see all the bits of fat speckled throughout the mass. The mass looks like a smaller picture of a breast placed on a larger picture of a breast.
My main concerns now is how much the dang thing hurts, the fear that it could continue to grow and grow (apparently they can get quite large), and the fact that I think I've got a second one in the same breast. There is already a noticable difference in size between my two breasts and if it gets any larger I will look into having it removed. Unfortunately it is really common to have them grow back though.
Also, hamartomas don't increase your chance of developing cancer. There is one condition called Cowden's Syndrome where multiple hamartomas grow throughout the body (including on the skin) that DOES greatly increase the rick of cancer.
I hope that helps,
Thanks,
Lori