if they were to run the models with a case count that was derived from the death toll, which is going to be a better metric than the testing anyways, then they'd get very different results.
guessing parameters is messy, and nobody is going to nail this. you need to expect large amounts of error.
but, this is certain: if you feed the model bad data by suppressing the testing, you're going to get the same garbage out that you put in.
and, it will not be the models that will be wrong. it will be the government that botched the response...