Coming in a little late to this, but I think it's worth looking at one more piece of the feat, which is the 'normal' behavior.
"Normal:It takes 1 minute to treat deadly wounds, and longterm care requires a medical bay or medical lab."
It doesn't say anything about the normally being unable to use a medpatch, only the amount of time required to perform the check. What it does say is that you lose the normal functions of the medpatch. It's a way of letting you use this skill in a pinch to give someone a quick patch-up.
Does it specify that you need a tool kit, or a Tool Kit?
What it says is "The DCs of most medicine tasks are based on the type of equipment used". Treat deadly wounds says "This takes 1 minute, and the DC is based on the medical equipment used."
That implies that medical equipment is required, since a DC without medical equipment isn't offered anywhere else in the rulebook. With the ambiguity, I think a GM could rule it a high DC (30+) at their discretion, but without errata I don't think there's a 100% satisfactory answer.