And why do you presume your sources are better.
Your source is a fringe twitter account, followed by alt-right accounts, cherry picking bits and pieces from journals. It doesn’t even properly link to the primary sources so I can’t even examine the the weakness/ context.
Worry more about my Jacobs’s sources contradicting your sources.
The diagonal entries are defined in another way. See the link:
https://en.wikipedia.org/wiki/Transition_rate_matrix#:~:text=In%20probability%20theory%2C%20a%20transition,Markov%20chain%20transitions%20between%20states.
Apologies, I could have made this clearer. It is only those diagonal entries which are allowed to be negative. In fact they must be negative (or zero).
Technically, the diagonal entries are transitions from state i to i (ie. they are not really transitions but rather a measurement of “retention”). You can think of the positive or negative sign as indicating if it is a measure of transitioning away from the state, or retention in the state.