If a unit test passes, what you can infer is - barred exceptions - that the unit tested works as intended. Nothing can be said about all other components involved since they might be (and usually are) faked.
Testers' confidence in the quality of a product, on the other end, is boosted by looking at acceptance tests. Such tests operate at a higher level and should cover the behaviour of the system when used by the stakeholder.
The question: Say you, as a tester, are about to release a new version of the software. You can choose whether to look at the status of the unit tests - which cover pretty extensively the system, unit-wise - or not.
Does looking at the tests have any effect on you? For instance: - how is your confidence in the quality of the release affected? - would you test differently (different approach, more in-depth testing of some component with respect to others, ...) if you didn't check the status of those tests?