I don't know where that point lives, but as NPRs expose demonstrates, that amount is certainly larger than zero and probably a lot larger than where we are now.
Also, since the purpose of the program is to reduce poverty, not to detect fraud, another effect is that the additional oversight will keep people away from the program, either by (as above) their inability to navigate the efforts to protect the program from fraud, but also by the effect of intrusive (and possibly personal and demeaning) questions and inspections has on people's self-image who choose to accept the aid (as per TFA), causing them to avoid taking it to avoid social stigma.
I know these are the types of points that laissez-faire libertarians laugh at i.e. "imagine someone who is taking my money refuse any indignity; they can always choose to starve," but those sorts of libertarians don't think that poverty is a concern anyway. When those types get to design programs like this, they end up largely populated by people who are willing to navigate them as a job, hence largely fraudulent, creating a self-fulfilling prophecy.
The vast bulk of overhead is ultimately fraud control in some form, and as that expands, so the program expands, while the number of people being helped stays steady or even shrinks. This massive administration is farmed out to contractors to reduce ballooning costs (cronies, friends of friends and/or benefactors - an externality that affects us all as a rise in corruption) who are rewarded for finding more fraud with a higher proportion of the budget of the program. Their primary motivation then becomes to find excuses to exclude people from the program.
This is depressing to even type. The reason one would have basic income is to eliminate this. I believe that every millionaire should receive a check. Means-testing is a scam.
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.