I think the metaphor is appropriate but misinterpreted.
One of the key attributes of rugby is that the team is composed of specialists who co-operate within a rigid structure, and the emphasis is on team play. You can get by on a running/kicking game or if you've a heavy front line just steam-rolling the ball, but the best teams master the continuum between both, and thus draws in the entire team to the simple goal of getting the ball over the line.
The actual "scrum" itself is where play restarts. Your scrum-half (not sure if this is the scrum-master or product owner - I feel the latter is more like the coach) puts the ball in, you all push and squeeze a bit the ball is released and play continues.
I think the scrum itself is meant to be the standup, though many other aspects of the process (refinement, retrospectives, sprint planning) create this "pressure cooker" scenario, where the team comes together in uncomfortable yet intimate circumstance (anybody ever played lock?) as a punctuation between plays.
I suppose the process could have more appropriately been called "Rugby" (glaringly absent from the metaphor is the opposing team though), but I guess Scrum was more catchy and is probably the most
salient attribute of the sport to an outsider looking in.