Palmer's point is that there is no "option" as to whether one joins himself to God in covenant, and there is no joining that does not embrace the body-soul complex.
This is not to deny that there are those outside the visible church who are united to Christ. But exceptions merely prove the rule. When exceptions are no longer "exceptional," this situation forms a true threat to covenant-expression. Instead of a "body" (which by the very terminology is clearly substantive), we have a "gas," the ephemera of Christ.
Palmer points to the phrase, "covenant in your flesh," by which Moses is seen to acknowledge that the ceremony or rite is itself the covenant. We can say the same thing regarding a marriage-covenant. The marriage, of course, is the deep and abiding companionship of two body-souls. But it is also the whole marriage ceremony. And it is the vows in particular. And it is the rings on the fingers, which are the covenant on/in their flesh. See the connection?
In circumcision, a tiny little "token" of blood is spilt, reminiscent of the dead animals and the pool of blood of the covenant-ceremony (cf. Gen.15). It's a permanent mark. It's a sign of the promise to cause the redeeming Seed to arise from this nation. The sign of the covenant is the covenant-visible, tangible. Just like the rings of a married couple. How badly do you feel if you lose your wedding ring? Just try taking that ring off for a few nights-out on the town--how's your spouse going to react?
We can add, finally, the fact that God makes promises by means of his signs. So, if anything other than Providence hinders us from receiving his sign/covenant/blessings-by-it, that's saying something about our valuation of his word of promise. We can take it or leave it. We claim the "reality," while his preferred means of self-expression to us isn't really that important to us. "Baby, we are really married in our hearts; I know your love is unfeigned and unmovable; your love makes mine possible; I can never abandon you while you hold me so tightly. You want a wedding to show that love, but how does that make it any more "real"? C'mon kid--we don't need the expense."