It's correct that by reducing your number of units and making them more broad scoped, you potentially reduce the number of undetectable faults you are catching (but need not), but you also make crafting the input that detects the remaining faults much more difficult.
The correct approach is (it seems obvious to me) to mix the two. Don't force tests to be on a per-method basis, but also don't neglect to individually test those methods that can be better tested by individual testing. It seems like common sense - following a policy such as this so rigidly clearly leads to either wasted time and inferior APIs or missed test cases - the former I believe the OP has discovered already, the latter I'm sure they'll discover in due time.
http://www.quickmeme.com/img/0f/0fb4fa35fad1b9ed112dc7584f47...