It's not about "testing in Italy":
"In Lombardy – despite the region being under lockdown since March 9 – more than one in every 1,000 of the entire population have already been hospitalised due to coronavirus."
An acquaintance's partner suspects having got it, because after two days (two days, not weeks) of very mild fever (~37.5C) he was hit by anosmia. An ex-coworker also mentioned "a horribly strong fever" with respiratory difficulties which lasted just a few days. Yes, anecdata, but shows that you can easily miss a large part of the infected cases if you only test those hospitalized.
To get such a count we would need 100% serological testing which has not been done. We know how many were infected at the time of testing but the whole point of the Oxford model is that we do not know how many have been infected, not shown symptoms, and recovered.
Once again, the core point of the Oxford model was to emphasise the need for serological testing.
We definitely know it’s higher than 1 in 1000.
Unless you all think that the number of people infected may be higher than the number of people.