"Heidegger was mistaken when he wrote that death in this sense is definite as to its that unless he meant that it is quite definitely possible."

Of course that is (sort of) what he meant.
It is a point about which he is explicit.
Death is one's ownmost possibility that is NOT a possibility.
And that is why confronting it results in Angst, rather than fear.
We fear THINGS.
NOTHING is another story...
The best way to remember it is that death is a situation without a situation,
there is no "I" to inhabit this situation, as the "I" is DEAD,
and as every situation requires something situated,
it is a situation that simply cannot be.
It is NOT a possibility...
Unable to put ourselves there, we become anxious...
Confronted with the necessity - that we will be in that situation however impossible it is (to conceive),
we feel Angst.

Heidegger is doing something very important here, besides telling us about death.
He is telling us something about how our minds work...
They work by putting ourselves into different situations,
understanding those situations on the basis of experience...
Which is why wisdom (experience of many situations),
and why authenticity (taking up one's own situation - including the NON-situation that is one's own death)
are so important.