LTT was only speculating, they did not know the actual price as far as I remember. (They had a video doing some educated guesses, or maybe a WAN show, can’t exactly recall).
No doubt the price was lower before this hardware shortage, but the $800 is not a reliable number afaik.
In their video today, they said they asked Valve the original pricing, and they said (paraphrasing) "we can't tell you exactly - but the increase we recently had on the steam deck is about how much the pricing for machine increased" - which is how they came up with the $800 number