Can I eat that without worry? I prefer it that way, and sear it on the outsides, but I'm not sure that it's safe. More or less raw but hot, on the inside.
Steak Tartare is served raw and providing basic hygene rules are followed, the meat should not be dangerous to eat.
I have my steak medium purely through preference not because I worry about eating "not cooked" meat.
I think there is too much variation on what different establishments call rare medium and well done. Personally I'd prefer they'd ask how I like my veg done, not my meat so much.