An acid will be 50% dissociated when the solution it's in have a pH equal to the acid pKa ('afirmation 1', for later reference).
We also know that a good buffer solution have equal concentrations of an acid and it's conjugated base.
That's why to make a good buffer we look for an acid that have a pKa close to the pH we want to maintain.
So, suppose I have a solution with a pH 6.2, and I want to add a buffer to maintain this pH at 6.2.
Suppose also, that I have a ideal weak acid for this situation: with a pKa of exactly 6.2.
Using the Henderson–Hasselbalch equation, we know that we need to have the same concentration of the acid and it's conjugated base in the buffer. To add the conjugated base, we use a salt of the refereed acid.
So my question is: If we just throw the acid at the solution without the salt, since the solution pH is exactly the pKa of the acid, the acid will dissociate 50% (afirmation 1), and we will end up with what we wanted: The same concentration of the weak acid and it's conjugated base.
So, in principle, it's possible to make a buffer without adding the salt?
Is this logic correct? If not, what error I'm making?