The following express contempt in varying degree for unsupportable claims, or at least a need for caution.
- Pure speculation (science).
- Unsupported optimism (science, engineering).
- Rainbows and unicorns (politics).
- Fiction presented as fact (politics).
- Lies, damned lies, and statistics. (politics - Benjamin Disraeli)
Another variant of "...out of thin air" uses plucked:
...while the underpinning notion is sound (that denser gases increase heat retention) typical climate models have been force-fitted to recorded data with constants and scalars plucked from thin air, and fail to predict even the past...
In this excerpt the meaning is "selected without any scientific basis".
And now, for your entertainment, the inimitable Sir Humphrey Appleby:
Unfortunately, although the answer was indeed clear, simple, and straightforward, there is some difficulty in justifiably assigning to it the fourth of the epithets you applied to the statement, inasmuch as the precise correlation between the information you communicated and the facts, insofar as they can be determined and demonstrated, is such as to cause epistemological problems, of sufficient magnitude as to lay upon the logical and semantic resources of the English language a heavier burden than they can reasonably be expected to bear.