Ah, but we’re not told that he was Italian - just that he started his journey in Italy.
He could have been rejected at Heathrow for a number of reasons.
One possibility is that he did not have a visa which he did, in fact, need to enter the US, and the airline rejected him. Strictly speaking he ought to have been turned away at Rome, but the airline carrying him from Rome to London may have been less vigilant about checking his visa status for his ultimate destination, the US, than the airline which would actually carry him to the US. This might be especially so if the Rome - London carrier was not a US airline, while the London - NY carrier was. (I think, but I am not sure, that carriers to the US are fined or otherwise penalised if they bring somebody to the US who is turned away at immigration for not having the required visa).
Another possibility is that he attempted to land (i.e. pass through UK immigration) at Heathrow and did not have a visa which he required for the UK. However a passenger in transit to the US would not normally need to land (in this sense) at Heathrow.
The general practice is that the carrier at the point of origin is supposed to check that you meet the immigration requirements for your final destination. This is especially so if you are being “checked through” to your final destination.
If you are turned away at an intermediate transit point, it is either because the original carrier failed to check properly that you have the visa needed for your final destination, or because you were not checked all the way through, and presented yourself at the intermediate destination to check in for the final destination.
Note that in all these cases it is the airlines who are doing the checking and the turning away. Generally you will not meet a US immigration agent until you actually land in the US. (Although there are exceptions - passengers travelling to the US from or through Ireland, for example, clear US immigration before they leave Ireland).
If you are turned away at an intermediate transit point, you can if you wish seek to be admitted to the country you are now in. If you choose not to do that, or if you are refused, it is the responsibility of the airline who brought you there to arrange for you to be brought back to where you started (or to some third country that will accept you). If this is going to take some time you may be temprarily admitted to the country you are now in. You may be detained, if it is thought that there is a risk that you will seek to stay illegally. If your return journey can be arranged within a few hours, you will probably stay airside like any other transit passenger.