Disproving form is a thing should not be particularly hard. You just have to check time correlation. If someone has done it and found no correlation between one innings score and the next, I would take it that form has been disproven. Looks like the thread that you share does that, haven't checked in detail though.
Getting set is certainly a thing. I have earlier tried to fit geometric distribution to the scores that batsmen get out for using Tendulkar as an example (because largest sample size). See
chart. This distribution assumes that probability of getting out before scoring another run is independent on the current score you are at. The distribution fits at most places but at the start of an innings the actual dismissals are more than those predicted by geometric distribution. See an old discussion on this
here.
The OP in the thread is only looking at Tendulkar. It's ridiculous to extrapolate from a single player to every player ever, and the choice is extremely questionable because he is the most famously consistent bat I know of.
In a purely statistical sense it's not possible. We will end up with a correlation, and we can interpret deviation, possibly to a satisfactory regard, which we could maybe simplify to proof in conversational terms rather than statistical ones. But there are too many extraneous variables with too great an impact to simplify it this way.
Take a simple, and very plausible example of a bat who averages 60 home and 40 away. He plays 10 consecutive home tests at an average of 60. An analysis that does not control for home/away average would interpret this as moderate? 'proof' that form exists, because this run of 20 innings@60 would likely fall outside of standard deviation despite being exactly average if controlling for home/away.
There's an infinite number of extraneous variables at play here that we could control for. Most of them will not have such an obvious impact, but there are some that we can't ignore. Opposition quality and style and pitch conditions are the most obvious that spring to mind. It might be possible to set up a group of control variables in a way that gives us an answer that we are comfortable with come close to a proof, but I'm not sure anyone has done this, or that anyone will bother.
The majority of players have notable protracted highs and lows in their careers. Almost everyone dips at the end before getting retired or dropped. I'm happy to call this form, and for me it is proof that form exists