This is under the premise that a player is already at a "maximum amount of opportunities". As such it is a thing that will first have to be proved, or the resulting theory has no basis in reality.
Another simple theory is that increased shooting can lead to an increased number of assists, both as a result of the shot, and indicrectly, because it might make the other team more uncertain as what a player will do, which might open up passing lanes.
I am not the man to figure out the statistics behind, shots, goals, assists and sh%, all I can do is to mention that there are individual examples of players increasing most all of those stats. Look at Daniel Alfredsson 2005-2006 for example: career high number of shots, goals, assists and the next highest sh% number. So, there are at least doubts about whether your theory is correct.
The example implies that things are not so simple, and that there are many factors to ponder.