The way you remove the needle in the beginning is not correct and actually dangerous for yourself and others.You should have your hand facing up lying in your free hand and place thumb and index of free hand on needle cap pointing same direction as needle then pull (only few mm). Then you can take off the needle entirely in the way you do here.
If we understand you correctly, you bring up a valid point about safe needle handling. The person in this video has her palms touching to prevent the reflex stabbing you speak of. Your methodology of needle removal is a good suggestion and with practice either approach should be safe and effective.
