Source on this?
A few years ago when the whole "people are tracking your phones using wifi probes!" story got popular I ran packet captures on an android and ios device and found that neither made directed probe requests (ie. the kind that contained SSIDs). The man page for wpa_supplicant (which is used for android) seems to confirm this:
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
themselves by not broadcasting their SSID require technique 1,
but beware that this scheme can cause scanning to take longer to
complete.
https://www.daemon-systems.org/man/wpa_supplicant.conf.5.htm...