well, could you try to repeat all actions as you've described in your video, yet with "Free" snap disabled and check results?
I suspect the situation is the following:
1) when you snap at 0:19 you try to snap to the endpoint of line (which is natural)
2) however, as free snap is enabled, reference point is snapped not the endpoint of line as you expect, but to some point that is on the left side from it.
3) for sure, the angle of line from that point to rotation center is different than the angel from rotation center to endpoint of line
4) due to different angles - you see that difference in rotation result.
The image below illustrates my considerations: