Automated tests are code too

There is no way of denying it: automated tests are also code. And any line of code has a certain probability of containing a bug.

Does this mean you should refrain from test automation? If so, it sounds like refraining from coding in general. For sure, the challenge is to keep the bug probability to a bare minimum by making the test design a part of the requirements and requirements review, by reviewing the test code like you would want to review the app code, and by making sure that tests always end with an adequate number of verifications by putting them under source code management.