All of the organic processes in ponds get VERY complicated very quickly.
One of the mechanisms by which adding barley straw to a pond inhibits some algae growth is based on the production of humic acid from the late-stage decomposition of the straw. Further, humic acid does tend to turn things brown.
If that is the current operating mechanism, then the humic acid MAY be killing a bit of algae and as the dead algae is decomposing it creates gas bubbles causing it to float. (And the humic acid and/or decomposition is turning it brown.)
When you said the pond was "clearing" with the barley straw out, did you mean the scum floating on the surface or the secchi disk reading was getting deeper?
If the latter, then my speculation is wrong. Or, some unrelated change has occurred contemporaneously in your pond.
Here is a basic primer on barley straw.
Barley Straw for Algae Control
