HP do not equal blood. "bleeding" in 4e is taking ongoing untyped damage. Unlike in 3e, you do not take a point of damage each turn you are dying [which was the risk of death for that game]. Instead you make "death saves". The idea of saving against death is not seen in the physical world outside of seeing whether or not you failed 3 [you die] or if you hit 20+ [you spend a surge]. Death saves are a random way of determining how long you "last" in your present condition, and a small chance of recovering without outside help.
When someone gets knocked down, while the PLAYERS and the DM know absolutely what condition that character is in, no one else knows exactly how bad things are except that the character is in bad shape and is AT RISK of death. Ultimately, everyone is dying until they are dead ... so it's someone who is NOT DEAD YET, and is waking from unconciousness [that never happens ... no one can black out for 6 seconds because of taking severe punishment, shake it off and get back into the fight again.]
Ultimately it ruins the narrative ... if you "write yourself into the corner". If anything that puts someone down without killing them should have killed them ... it's going to seem very odd that they aren't dead. That has nothing to do with 4e. If you describe the condition that makes the character dying in such a way that you cannot except that a warlord's cry could bring an unconcious character back into the fight ... I think it's pretty clear where the disconnect lies.
EDIT: In Regicide's specific example, the dying character is described his wound bleeding heavily. That is something extraneous that has nothing to do with dying/unconciousness. How is it unbelievable for someone to get back up after that but it ISN'T unbelievable that they take NO DAMAGE from the bleeding wound? Without an ongoing damage (save ends) effect, you don't really have life threatening bleeding. So, eliminating that from the equation, you have a condition where someone takes some severe damage and collapses as a result of it. It may seem like they've been severely beaten and bruised and rendered unconcious. However, they get back up ... STILL beaten and bruised, but they've regained conciousness.
Most HP damage is superficial at best ... because no matter HOW beaten up you are, you suffer no penalties for being bloodied [which is different from bleeding] outside of either being angry [as a Dragonborn, etc] or being a better target for the monsters [vs. Tiefling, etc]. However being at 1 HP is not much different from being at full HP. So, your wounds are CONSTANTLY closing themselves up, clotting, etc. Ongoing damage [specifically untyped damage] is used to specifically describe a bleeding wound. They also have conditions to describe other types of injuries [dazed, stunned, slowed, immobilized, weakened, penalties to attack, penalties to defense, etc] and all of those are similarly defined as temporary, either for a turn, or until save ends. In those cases you get more specific types of injury that cause mechanical problems other than getting someone closer to unconciousness and making death saves [being at risk of dying very soon].
