I'd say it all depends. Seems like what you are describing certainly comes into play with some recruits (especially QB's in football), but a lot of recruits it probably doesn't matter to. Based off the comparable rankings, I doubt Adams is watching what Wood does. But Wood may have been told that if Adams commits before him, there might not be a spot.
There are several different types of offers - the top guys get offers that are basically we will take you no matter what, middle guys get offers that say we would love to have your commit - but your spot might disappear if someone else commits first, and the lowest guys get offers that say we think you are good enough and love to have you, if we have space at the end of the cycle.
I imagine there is also a wide variation in how well/honestly the strings that are attached to offers are communicated by the coaches.