This is an example of what makes it so hard to communicate security advice to laypeople: nerds come out of the woodwork trying to reconstruct and critique the advice from first principles, and going off on all sorts of weird tangents.

So: no, nobody serious trusts Symantec. But not because they're "installing backdoors"; it's because their software is complicated, embedded deep into the guts of the operating system, is historically full of bugs, and doesn't actually solve the problem it purports to solve.