You are correct. Sorry! I thought I remembered part of the video being internet free, but apparently not… 
What I can offer instead is this, which I just tested, and is almost internet free:
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Initial Setup - several Wyze v2 cams (stock 4.9.5.111 firmware) are WiFi connected to a router which is being fed by hard line internet. The Wyze cams have SD cards and are set to continuously record. Everything is authenticated and running as in a normal situation.
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Android Phone Scenario
Android 6.0.1 cell phone with both cellular data ON and WiFi connected to the same router. The phone’s Mobile Hotspot feature is OFF.
Action - Physically unplug the internet feed from the router. Cams are still WiFi connected to router.
Action - Close all apps on phone, then open either the Wyze app or tinyCam Pro
Result - it takes several seconds but both tinyCam Pro and Wyze apps appear to work fine - streaming live view, SDcard playback, viewing 12 sec clips
Conclusion - the Android phone authenticates with Wyze servers and views 12 sec clips via cellular data, but communicates directly over the WiFi LAN for live feed & SD card viewing. No new 12 sec clips are being recorded to the Wyze cloud.
Presumably this means that no Wyze cam private video data is leaking out to the internet cloud.
So in theory the cams are effectively no-internet, but the viewing phone still needs to authenticate with the Wyze mother ship.
Or the phone is doing some weird bridging that shouldn’t be happening, especially with the hotspot feature turned off??
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Apple iPhone Scenario
iPhone with both cellular data ON and WiFi connected to same router. The iPhone’s Mobile Hotspot feature is OFF.
Action - Physically unplug the internet feed from the router. Cams are still WiFi connected to router.
Action - Close all apps on iPhone, then open the Wyze app
Result - Bupkis
Conclusion - Apple thinks differently
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Using WiFi only, no cellular, both phones were total fails.
And I forgot to turn off cellular date during viewing to see how long the stream held - humanoid reality intruded upon my hobby yet again. 
So I’m pretty sure you can leave the cams internet free once they are authenticated, go away, and then come back and view them ( live stream and SD card ) - as long as you have an Android phone with cellular data turned on.
But I welcome any more accurate information! 
There is also more info on keeping Wyze cams away from the internet here:
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Are you wanting to POE these Wyze cams to your NVR with no WiFi at all and then stream that to a monitor/TV? Like a real security system? 
Or just WiFi the cams to an NVR and then to the TV, but this whole system is completely disconnected from the internet at all times?
I think you need Dafang Hacks RTSP firmware for that instead of the current Wyze RTSP offering…?