Absolutely there is huge sampling bias in testing. This is true over the entire world.

No one knows what percent of the broader population in Italy have been infected, asymptomatic or otherwise.

We can hope the number is closer to 1 million or 10 million than it is to 100,000. Because you can’t hide the severe and critical cases, a wider incidence means a lower severity. But we have no scientific data on this absolutely crucial statistic.

The only proxy we have is the positive rate for tests that are performed. Recently it was reported that the positive testing rate in NYC was as a high as 28%. This implies that the general population infection incidence is extremely high, e.g. several million cases in NYC. Ideally you would want to see a positive test rate closer to 1-3%.

Is that realistic? Many of the most vulnerable people are in nursing homes with a lot of younger staff, or else they have to go to the doctor/hospital frequently for other reasons. It’s hard to see how it won’t end up infecting a huge number of these people if we let it spread at the max rate.