Well i guess it depends. If you can figure out what the underlying problem is and identify a better solution then you have a number of options. You can provide several quotes for how much work will be involved, naturally the dumb solution will take longer. :-) Alternatively you can simply implement your own solution as a "proof of concept" and then point out they can have it Right Now, or wait some time for the dumb solution.

Another approach that works is use deductive reasoning to identify potential issues in the design, then write a very carefully worded mail saying that you wont procede until the issues are resolved to your satisfaction, or until a manager provides you with written instructions stating that they understand the issues that you have raised and want to go ahead anyway. This is useful because very few people like this want to be put in the hot seat. By forcing them to provide documentation you are making clear that in no way in the future will you be held responsible for the poor design, and that instead they will.

I suspect the truth is tho that the only really good solution is to find a different place to work.