I hesitate to stick my had above the parapet, but I wonder if those who feel another's pain actually cannot walk when someone else breaks a leg, have to take painkillers when they think of dreadful injuries.
How many of them wake in the night to tears and the utter desolation of knowing that they will never see someone again, never speak to them, never hear their voice?
They may imagine someone else's pain, remember how it felt when the same happened to them, feel distressed at their situation, weep for them, but physical pain is in the nerve endings, emotional pain in the impact on that person or the links that a bereaved person had with the one they lost. Someone else can only partly join them.