Can Deny Death and Die Hard work together?

[Cainus]

When you drop unconscious do you have to use Die Hard? Can you choose to instead make the stabilization check to get the healing from Deny Death?

Deny Death states:

Spoiler:

Benefit: As long as you have 1 ki point in your ki pool, when you fail your Constitution check to stabilize, you do not lose 1 hit point. If you succeed at the check, you can spend 1 ki point to heal 1d6 hit points. If you roll a natural 20 on the check to stabilize, you can spend 1 ki point to heal 2d6 hit points of damage instead.

And Die Hard states:

Spoiler:

Benefit: When your hit point total is below 0, but you are not dead, you automatically stabilize. You do not need to make a Constitution check each round to avoid losing additional hit points. You may choose to act as if you were disabled, rather than dying. You must make this decision as soon as you are reduced to negative hit points (even if it isn't your turn). If you do not choose to act as if you were disabled, you immediately fall unconscious.

When using this feat, you are staggered. You can take a move action without further injuring yourself, but if you perform any standard action (or any other action deemed as strenuous, including some swift actions, such as casting a quickened spell) you take 1 point of damage after completing the act. If your negative hit points are equal to or greater than your Constitution score, you immediately die.

I'm not sure if I can choose which feat to use.

[Matt Stich]

I would say no because you automatically stabilize. Deny Death would never trigger because you never have to make a stabilization check.

[Cainus]

And yet the feat Survivor seems to imply that you still may need to make stabilization checks even with Diehard:

Prerequisite: Con 13, Diehard, Endurance.

Benefit: You gain a +5 bonus on all Constitution checks made to stabilize while dying.ce per day, if you are struck by a critical hit or sneak attack, you can spend an immediate action to negate the critical or the sneak attack damage, making the attack a normal hit.

The feat requires you to have Diehard, but it still grants a +5 bonus to stabilize.

Granted this could be a result of Developer oversite.