I was taking the most simplistic approach. Your point is better than mine, but usually the argument I see is that "there are welfare queens, and that's not fair, therefore there shouldn't be welfare at all." I was more arguing against that.
Unfortunately good government requires carefully understanding and administering a bureaucracy, taking into account individual incentives, and building something non-simple.
Basic income is just a cheap mental hack used to seduce the lazy. It's like looking at a webapp, realizing that 75% of your compute cycles are doing error handling and then saying "aha, the solution is to ignore all errors!" It's seductive, brilliant in it's simplicity, and complete idiocy.
Among other things, this is why essentially no basic income proponents are willing to even do a back of the envelope calculation to show how it would work. (Similarly, "eliminate all error handling" guy will refuse to write a proof of concept.)
[edit: I altered this comment to explain in better detail what I think is wrong with BI, but eliminated a sentence that SandBOx replied to. I believe the real goal of most BI proponents is to create a vote bank of government dependents.]
It's a reform of the French tax system based around a basic income and flat taxes on income and wealth. The resulting redistribution is similar to the current system without the nasty border effects and bureaucracy.