You can think of a body shop as a workplace that handles bodies — not engines, not ideas, but shells. A car rolls in with a bent door; the shop straightens the metal, fits a new panel, sprays the colour back on, and sends it out again. The shop does not own the car and does not keep it. Things come in damaged or idle, get handled, and go back out.
From the picture
把人租出去的公司
同一個畫面換成了人：東西進來、被處理、再送出去。這裡送出去的是工程師的工時，公司自己不做產品，只把人一批一批派到客戶那邊。用 body 來稱呼人，語氣本來就不客氣，所以這個俚語常常帶著批評。這是理解上的連結，不是在說歷史上誰先誰後。
noun · C1
In business slang, a company that hires workers — usually computer people — and then sends them out to other companies for short contracts, instead of doing any work of its own.
人力外包公司
noun · B2
A garage where the outside shell of a car is repaired — the doors, panels and frame — usually after a crash or a scrape, rather than the engine inside.
車體維修廠（板金烤漆）