I don't think the coding test isn't there because people think you're lying, it's there because we have no industry wide, respected entrance exam. Actuarial interviews don't (to my knowledge) contain a whiteboard vector calculus exam, but this isn't because people just sort of believe actuaries, it's because you have to pass a rigorous exam on these topics to become an actuary. I sometimes wish we had something like this in our field (not necessarily a legal requirement, just something that is widely recognized as legit). I'd be happy to put the time in and really study for a proper exam, but I'm not as interested in doing this over and over for companies that may administer and conduct these exams frivolously and in secret.
Also - I actually do agree that it's bad if someone can't write fizz buzz, but every interview exam I've taken has been vastly more difficult than fizz buzz. It's "find all subsets of a set of integers that is divisible by the sum of a different subset of integers". At a whiteboard, in 45 minutes. These aren't impossible problems, but they're much tougher than fizzbuzz.
I am saddened, angry, and relieved to hear of your problems with homework. The response you got back makes me realize that the two times I've done a homework assignment were probably pretty typical. I won't do this anymore, and I do accept that this will limit my career options. It does anger me, though, when the companies who do this complain about a shortage of engineers.
True story: I did an on line exam and take home homework assignment, waited over a month (crickets chirping) to hear back, pinged the recruiter politely now and then, and finally got a one liner "we've decided not to continue at this time.' A few weeks later, an article with came out with a picture of the CEO of this company standing next to President Obama, who nodded gravely as the CEO talked about the desperate shortage of software developers.