Stagnation point on swept wings
 

It was recently explained to me that one of the reasons for washout on a swept wing is that the stagnation point (point at which the airflow separates to go either above or below the wing) moves from in front of the leading edge near the wing root to under the wing leading edge near the tip.

Is this correct, and if so why does this occur?

That sounds about right to me. Stalls on a swept wing airplane will progress from the tips to the root. The washout would give it more favourable stall characteristics.

This is a good reference: http://www.faa.gov/library/manuals/a.../00-80T-80.pdf