This description is misleading and almost entirely incorrect.
Si is not really physical. I would never say that Si means being in tune with your body. Si is only "physical" in the sense that it is based on sensory memory, and not on intuition and connecting dots (the dot-connecting is Ne). Sometimes it is like a gut feeling, but it's a gut feeling based on prior experience -- you may not remember that experience right away, but that precedent is constantly being referenced. The experience could have happened to someone else, in which case the experience is only sensory because you heard (with your ears) or read (with your eyes) someone discussing it.
Si is like being chained to an encyclopedia, or a filing cabinet full of documents. Before you can act on anything, or come to any conclusions, you have to reference those documents. All of your internal definitions are based on those documents. If one of them is rendered invalid, you have to put a replacement document into the same slot. Every single event that has ever happened to you, that you've ever read about, that ever registered with you in passing, is present in those documents -- and you may not even realize that you're referencing them, when you're referencing them. Only sometimes will an Si-user consciously think "What did others do in this situation, that I can learn from?" The rest of the time, it may, as you said, be a "gut feeling" -- thinking "that's unusual", because you've never seen anything done like that before, but not consciously going through every contrasting experience before thinking that.
The hammer is Te or Fe, not Si. Si is not about action. Si is about collecting and referencing data. Your "bull in a china shop" metaphor is much more about extroverted functions being backed by Si, than it is about Si itself.
Here's my favorite explanation of Si (in contrast with Ni):
As in the other thread, great clarifications. Thanks! So, following on from your thoughts . . .
One might expect people with strong Si to be much more interested in knowing things for the sake of knowing it, but I find it's the introverted intuitive types who seem to be most interested in in an idea or a fact simply for the pleasure it brings. How would you describe that process of taking in and cataloging all that data? Is it largely automatic and unconscious? If it's conscious, is it completely neutral, mechanical?
I don't know if I'm quite ready to acquit Si for it's role in the ESTJ's force of will just yet though ;-) You are correct that it's more precise to point out that the action part of that archetype is Te; Si is only responsible for the warehousing. I have had conversations with ESTJ's about painful past experiences, however, and I was struck by how nakedly painful it was to revisit those memories. The familiarity, I think, is key. I can see how a determined Te being multiplied by the visceral immediacy of Si would give the ESTJ more spit and vinegar than the average person.
Mind you, I'm also relying a bit on some logical leaps, perhaps. I find it really pretty easy to forgive past hurts, and I don't spend really any time dwelling on the past. 8th position Si has got to be good for something. lol
Have you done much with shadow functions and projection? I know how an ESTJ's 7th function Ni came across to me, a Ni dom. I'd be curious to hear from you (or any other ESTJ) what 8th position Si provokes in you as a reaction.