That is why they are doing trials. There is strong anecdotal evidence, but those datapoints were not done in a way to definitively determine the safety and efficacy of the medicine. (In other words, does it work, how well does it work, and is it safe.)
One part the rest of the world has done very well that our FDA has sucked about is weighing the balance appropriately between being 100% precise and wasting time. For example, these drugs have been on the market a long time and the side effects are known well. If you target people that are in very serious condition in the first place, what have you got to lose? Nobody is advocating prescribing this across the country to everyone yet. What the aggressive folks are saying is lets be responsibly aggressive - target those in most need with nothing to lose and do it in a way so that when we're done with this next phase it meets all the protocols for the FDAs requirements to approve for a larger use of it.
Traditionally, the FDA has stood there stoically with its arms crossed saying No. No bending or changing of any rules until they 100% know everything about a drug. That's why even the most world renowned epidemiologists in the world still have a lane they need to stay in.
except for the part about being reckless. Trump isn't advocating the spread of the medicine across the country. He's been pressing the FDA to be more aggressive in allowing trials to go forward. His justification is that its a drug that is well known and been around for a long time, so the side effects are known well. "What have we got to lose" is his non-scientific rhetorical question. My gut tells me we will find medicines and vaccines from other countries first, because our traditional FDA posture is so restrictive. Its well intentioned, but often too restrictive, as we learned during the testing fiasco we've faced. Then we'll be faced with the question, do we allow what other countries are doing to be done here? That's also traditionally been a No, until we do it ourselves.