At one shop where I worked we used the phrases "A good integration test is worth a thousand unit tests" and "Unit test that which cannot be easily tested with an integration test." I guess they had issues with people writing unit tests that were effectively testing getters and setters so they were trying to swing the pendulum hard the other way... but it also somewhat makes sense: invest your test writing where you get the biggest bang for the buck time-wise.
I like those quotes! I may borrow those if you’re ok with it.
And I agree with trying to find the best bang for the bucks. Especially if your project existed without tests at any point. You’ve got to pick and choose wisely.