what is the meaning of the cryptic formula in the 4sp satipatthana formula? (for the Chinese parallel)
"seeing body as body" and "body in body" both means "seeing the body according to reality as it actually is". This is to see the body without any additional interpretations or view. Essentially seeing what is there as it is.

This does not mean "you contemplate body in isolation of the 3 other frames of 4sp". You can choose to if you want to as your main focus, but any of the 4sp one cannot do purely in an isolated manner as one influences the other. E.g. if you are doing kayanupassana this influence vedena. Following highlights how the 4 elements (part of kayanupassana) influence feelings.


  vedana can certainly be connected with three of the four mahabhuta (elements), which are collectively known as rupa. These three are pathavi (earth element), tejo (fire element) and vayo (air element). Apo (water element) is too subtle to touch, or is so subtle that one finds difficulty in feeling it. Now, to illustrate the connection between vedana and the three bhuta, when you have a cramp, which is the tightening of the muscles, it is pathavi; when you feel temperature of the body it is tejo; when you suffer from pain in the stomach, it may be something to do with vayo, for when the air in your stomach is stuck and finds no vent to get out, you have that experience of unpleasant feeling called pain. The connection of vedana with these mahabhuta makes it all the more manifest and helps one realize its true nature.


Source: Vipassana and Vedana as Understood by a Novice by U Tin Lwin