This is a good, 11 tweet summary of why the science really is testable, falsifiable science https://twitter.com/ClimateOfGavin/status/121788547450272972...
As in, 8 iterations of Moore's Law before the present day.
If there were problems in those models, you could show them today with just a few EC2 instances on Amazon Web Services. You would not need a supercomputer.
"It is difficult to get a man to understand something, when his salary depends on his not understanding it."
- Upton Sinclair
"It is easy to get men to claim something, when their salary depends on them making the claim."
As supporting evidence: Statistics.