Dave S: Storm water overflow does not cause beaches to be closed. Raw
sewage
does.
You don't need to see solid matter for the sewage to be present.

Older cities have combined sewer/stormwater drainage systems. During
periods of heavy rainfall, CSO (Combined sewer overflows) occur in these
older systems, because the sewage treatment plant can't handle the
increased flow. Therefore, heavy rains do in fact result in raw sewage
draining into lakes, or rivers.

This problem violates EPA discharge laws. The offending systems are often
sued by the EPA to get into compliance. They then enter into Consent
Decrees with EPA to construct suitable upgrades.