This is an extremely serious charge - but also goes to show how much false information folks on the internet put out.
Based on my own review, at all times that SpaceX launched they have had a license to do so. Period.
The license is LRLO 20-119.
Could they have violated a condition of the license? Very possibly. But this claim that they launched without a license seems like a total lie.
The other issue, looking at the condition they may have violated.
1) They had repeatedly complained about the software model being used as being inaccurate. The FAA has not as far as I known really defended their model.
2) This model reflected a view that the weather would "amplify" an explosion. The physics of this seem at first glance a bit out there. Some effect seems possible, but a major effect seems somewhat less likely. Anyone want to chime in.
3) SpaceX had offered to work with FAA on better modeling / more data collection, but that had not been accepted by FAA.
SpaceX was shut down for something like 2 months as a result of this. My guess is there relationship between SpaceX and FAA also harmed here.
Hopefully someone on FAA side can go through model so that there is increased confidence SpaceX side that it is kicking out real risks. My impression as there was a lot of engineering frustration about the FAA model.