In fact it aligns with my thoughts. So pulling in some points from it here: (1) You don't want to show every dependency on a UML diagram - there are far too many. You need to be very selective and show only those that are important to whatever it is you are communicating. (2) If there is an association between two classes, there is also a dependency. The association implies it, as does a generalization.
Class diagram example of association between two classes.