Friday i was diagnosed with a broken blood vessel or vein on the top of my foot after no recollection of injury. now, it is bruised and the vessel is swollen and purplish. the bruise itself is spread and greenish. can this happen without trauma?

Yes: Sometimes you do not recognize the initial trauma. Bruises will spread and change colors like this and then should fade away after a few weeks. If it becomes increasingly painful you should see a doctor.

Damage control.: Don't kid yourself, almost everything you do causes some sort of trauma to your body. Thankfully the vast majority of the trauma is microscopic in size. Your body is able to deal with the damage without incidence and in all likely-hood you would not even notice the reparative processes taking place. Your bruise is an indication that the trauma was there but not severe enough to notice.