Yeah, that's a good point. They were, sometimes, a little too stringent on security.
Part of it might be that you can't just discredit everyone as "crazy." I mean, you might have a guy whose friends know him as a very sane, very rational, reasonable person. And so, when he starts sanely, rationally, and reasonably explaining the existance of aliens, his friends, at least, might grow suspicious. And then they'd spread the word to their friends, and so on.
And even if you actually do manage to write off all the whistle-blowers as "crazy," you would still have the problem that all these so-called crazy people are using the same terms over and over. Hmm, how come all these different psychos are suddenly talking about Yeerks and Hork-Bajir?
There's plenty of conspiracy nuts out there in the good 'ol human race. There are loads of people who would spot those inconsistencies, and leap to exactly the correct conclusion: that there's an alien invasion, and that it's being covered up. Yeah, one or two conspiracy nuts probably wouldn't be a problem, but if you get enough of them, and they band together . . .
As a final note, I would like to point out the website in book #16. As crazy-conscious as the Yeerks were about security, they apparently still managed to not even be careful enough.