If it's not too hard to do, then it's not too hard to go ahead and test whether the solution is any good - you have to validate through testing because something being in print does not necessarily make it accurate. Going ahead and testing may require the boss's cooperation, though. If the boss is a pretty forceful type who has made up their mind, trying to go through your boss may not be a good career move for you.
You could try having a colleague going through their own boss and test the solution, or you could escalate the attempt to the boss's boss - be very careful how to phrase to the boss's boss if your boss is a forceful type who takes it personally when subordinates try to go over their head.
As you can see, it's a fair amount of effort and initiative on your part. You are going to have to decide whether the problem is serious enough that it's worth it for you to apply this initiative and effort. If it's a trivial matter, I'd drop it for the time being.
If it's not a trivial and in fact, it's a serious matter, recall that the boss stuck their neck out and made the decision against going forward. Live with their decision, it's your boss's neck not yours. I had a CEO who was not above lying and lying pretty shamelessly when things went wrong. Immediately after he made a stupid and arbitrary decision, I would send him a follow up email restating what the CEO had decided and cc: ing those of my colleagues who were in on the action. Those emails kept him honest - just barely.
You must decide when you have done all you can and the battle is no longer yours to fight. In general, I don't obsess about saving people from themselves when they are hell bent on doing what they are doing.