Is integrity testing reliable ?

The quick answer is yes, when performed with an automated integrity test system and truly it does not matter of which particular brand, when used correctly and according to the manufacturer. The brands compete against each other, often claim a better test method and highest sensitivity, but well physics is what it is, you cannot twist it or make one part of it better than the other.
Anyway, back to integrity testing reliability. Integrity testing has developed over the last 20 years to a state of the art refined technology, with high accuracy and robustness. Testing especially sterilizing grade filters is of utmost importance to verify that these filters have not been damaged during use. So the test machine, but also the method and end-user training requires to be robust to achieve the reliable test results. The test should not be rushed, as it once in awhile happens, because saving test time, seems to be more important than a precise outcome, besides a failed test will cost by far more than time. There should be no shortcuts when it comes to appropriate wetting of the filter, training of staff, proper test gases and temperature conditions etc. When the test is properly qualified and performed, reliability of the test does not need to be in doubt.
Having said this an integrity test does not replace process validation of a filter. Process validation including product/process related bacteria challenge testing is the only option to verify that the filter is retentive within the process conditions filtering the defined fluid.
Integrity testing does not replace the necessity of the challenge effort. The integrity test is there to test the validated filter, i.e. the state of that filter in that validated process. Nothing more, nothing less.