CrazyEddie
Full House
I could be mistaken, but I think the digital card data needs to be manually fed into the stream recording graphics by somebody who has access to both (who presumably is in the control room). I don't think that transfer happens automatically.
The process almost certainly is at least partially automatic, with the card data being automatically populated into the graphics software so that the technician doesn't have to manually type in what everyone is holding. However, the action almost certainly has to be entered by the technician manually. The graphics software uses the automatic card data and the manual action data to determine what the correct graphics should be at any point in time (including creating the cool animations when hands get folded, etc), and the software feeds the graphics into the video mixer which adds it to the recorded video stream.
The technician almost certainly has a way to manually override the automatically entered card data, in order to correct a bad read (whether reading the wrong card, or having blank card data). This manual overriding doesn't happen often - usually the read error is a blank read, and the fix is to have the player try the read again so that the data can be automatically entered like normal - but it does happen on occasion and you can see it on the stream when it does. The graphic will have the wrong data, and then the graphic will go down, and then the graphic gets redisplayed using correct data (usually because of an all-in and a call with the cards revealed).
So, having a technician present in the booth with real-time access to the card data is an important part of ensuring that the graphics are displayed correctly. So, yeah, there's a guy in the booth who can see the cards and that's probably not gonna change, maybe not ever.