And what happens if under
(rightclick >) Options > Preferences > Subtitles > [Online subtitles]
you also
deselect "[ ] Download only if local subtitles are not available"
(It is possible that you first have to close and restart BS.Player.)
Only if the above doesn't help: (rightclick >) Options > Preferences > Subtitles > [Subtitle properties] Select "[V] Subtitles disabled" 
P.S.:
What version/build of BS.Player are we talking about (depress [F1])?
(This used to be a bug in a previous version.)