Medical debt doesn't go on credit reports, so generally speaking they don't really push since there's little teeth to bite with. I've had a LOT of debt on me, and I've dealt with many debt collectors, as well as someone with a ton of medical expenses - all I ever received was letters on those, as opposed to the aggressive calls related to other debts.
Medical debts show up on your credit report just like any others once they go into collection.
The newest version of the FICO credit score[1] does differentiate between medical and non-medical debts, though, where previous ones did not, and it weights the former less severely.