Kesubos 67b - Embarrassing vs. Killing

The gemara cites a story with Mar Ukvah where he and his wife jumped into an oven in order prevent embarrassing the poor person that they gave money to. The gemara says that the reason they took such extreme measures is that one should throw themselves into a fiery oven rather than embarrassing someone, as we see that Tamar was prepared to die in order to prevent embarrassment to Yehuda.

Is the gemara saying that Mar Ukvah actually jumped into an oven that under normal circumstances would kill him and was actual suicide, just that he was saved through a miracle in the zechus of tzedaka, or is the situation of Mar Ukvah not quite a "fiery furnace" and although uncomfortable, it was not suicide? Based on the second possibility, it would seem a bit strange why the gemara asks how they were able to do this. But according to the first possibility, it doesn't seem to be so parallel to Tamar. Seemingly, embarrassing someone in public is EQUAL to murder, not more not less (as Tosafos in Sotah 10b seems to assume). Therefore, one would be obligated to allow themselves to be killed passively rather than actively embarrass someone, as we find by Tamar. But, one would not be obligated to actively jump into an oven and kill themselves as Mar Ukvah did, in order to prevent embarrassing someone passively. Just as Tosafos explains in Yoma, that one does not give his life to prevent someone else from being killed passively since we say the opposite sevara of the gemara, "who says his blood is redder and his live is more important, maybe my blood is redder and my life is more important". Here too, Mar Ukvah should have said that his own life is more important than the embarrassment of someone else.