scan_ssid
SSID scan technique; 0 (default) or 1. Technique 0 scans for the
SSID using a broadcast Probe Request frame while 1 uses a
directed Probe Request frame. Access points that cloak them-
selves by not broadcasting their SSID require technique 1, but
beware that this scheme can cause scanning to take longer to com-
plete.
So presumably a (default) broadcast Probe Request would not disclose saved network names but somehow this doesn't appear to be true? Hence my question?
This may be a bug in wpa_supplicant, I'm not sure. I looked at the code, and it seems to be trying to avoid using the SSID in a probe unless this value is set to 1, but the code is structured such that the check needs to be done in many places so one of them may have omitted it. Should be in scan.c.