I suppose all those quoted cautions would depend on the meaning of "pumping". I don't think advancing the throttle from idle to about 1/3 open would be "pumping". I don't even think that advancing the throttle from idle to full open would be pumping. If it's not pumping to do it once then does it become pumping if it is done twice?
Maybe I won't have the O-360 much longer and this will all be moot. I have more fun with my much newer IO-360 which has no primer or throttle pump. I also get to write my own AFM so the start procedure can be whatever I'd like it to be. That engine starts in about 2 seconds hot or cold too.