Purple2153 is correct. Wi-Fi scans only include probes with network SSIDs if the phone has a hidden network in its saved networks. This behavior applies to modern Android and iPhone devices, which have included a series of Wi-Fi privacy features for many years now.
I'm surprised the guest in the video doesn't clarify this about hidden networks in the talk or in his presentations on the same material at Black Hat 2022 and CactusCon 10. This behavior is quite limiting from a tracking perspective as hidden networks are relatively rare.
Below are sources that confirm this.
From GrapheneOS's Usage guide:
Avoid using hidden APs (i.e. APs not broadcasting their SSID) since all known hidden SSIDs end up being broadcast as part of scanning for networks to find them again. SSIDs are not broadcast for standard non-hidden APs. Hidden APs are only hidden when no devices are connected. It makes little sense as a privacy feature, especially for a non-mobile AP where knowing the AP exists can't be used for tracking it since it doesn't move. The feature reduces your privacy rather than increasing it. If you need to use a hidden AP, make sure to delete the saved network afterwards.
The AOSP code for Wi-Fi scanning only includes SSIDs of saved hidden networks in the scan:
https://cs.android.com/android/platform/superproject/main/+/main:packages/modules/Wifi/service/java/com/android/server/wifi/scanner/WificondScannerImpl.java;l=179-213;drc=c36631df460411f7be385199e2e32b80211d6abe
As expected, the code is the same for GrapheneOS:
https://github.com/GrapheneOS/platform_packages_modules_Wifi/blob/16-qpr1/service/java/com/android/server/wifi/scanner/WificondScannerImpl.java#L179-L213
For iPhones, see Apple's "Wi-Fi privacy with Apple devices":
Wi-Fi networks are identified by their network name, known as a service set identifier (SSID). Some Wi-Fi networks are configured to hide their SSID, which results in the wireless access point not broadcasting the network’s name. These are known as hidden networks. Apple devices automatically detect when a network is hidden. If a network is hidden, the device sends a probe with the SSID included in the request—not otherwise.
If a phone doesn't have any saved hidden networks, this passive form of tracking will not work.
If a phone has a saved hidden network and that network has a unique name, this tracking would be effective. If a phone has one or more saved hidden networks and those network names are all common names, this tracking would also be effective. Even a small set of common names for hidden networks is enough to form a unique fingerprint.
The details above only apply to probe requests. If a phone has active Wi-Fi connection, provides a hotspot access point, etc., other forms of unique identification are possible.