I don't think anyone knowledgeable is assuming reported cases make up all or even a significant proportion of infected cases (I myself am in recovery from moderate lung inflammation which is probably COVID-19, but even with very-obviously-not-regular-flu symptoms don't figure in my country's stats because tests are reserved for those requiring hospitalisation)

Even if it was actually the case that nearly everyone in Italy had it in which case the casualty rates would be much lower than current estimates, the proportion of cases needing ventilators is sufficiently high to overload Italy's healthcare system (so the risk is similar, we're just looking at different risk factors i.e. the disease being less deadly but much more efficient at spreading than current estimates). Knowing that would make it easier to shift from containment to building more ventilators as a strategy, I guess

> I don't think anyone knowledgeable is assuming reported cases make up all or even a significant proportion of infected cases

The WHO explicitly and repeatedly asserted exactly that.

Surely the amount of symptomatic but untested people in Italy is high. If you're sick but readily able to manage the symptoms, and you're already under lockdown because the health system is overloaded, you're not going to bother going in to get tested - you're going to let the doctors work on the people who need it.