I definitely concur with this. Acceptance tests are really powerful as they somewhat "imply" unit tests. Using your gut-feeling to write them makes the process less brute force than "proper unit testing"
As projects get older I find that the acceptance tests are the part that change the least. Lower level there's always a degree of churn as you refactor out duplication, consolidate interfaces etc. and the tests have to be rewritten as you go. A good solid set of acceptance tests means you can refactor away without having to worry about breaking the site.