This would be True only if you have grouped the Projects by Status.

If you move 'AGR - S00066 - Sales Order' to another kanban Stage in above scenario, the Status will actually change - because the Stage actually reflects the Status.
A more obvious example would be to group Projects by Project Manager. Moving 'Renovation' from Stage 'Mark Demo' to 'Mitchell Admin' in below example will actually set the Project Manager to 'Mitchell Admin'. But - nothing else.

The question you are talking about specifically refers to Project Stages - as a dedicated 'Stage Stage': https://youtu.be/8yzslSQbg-s?t=60, thus changing the '(Project) Stage' Stage does not affect the Status:
