I get very cynical about any report that says "borders being closed" or "Schengen suspended", especially from the English-language media. It is because I live very close to a border and know the practicalities. Schengen has been in place over 20 years. In that time new cross-border roads have been built, border posts have been pulled down to speed up traffic, new bus and train services have been introduced across borders and cross-border commuting has grown immensely.
It is simply not practical to re-introduce the old checks of everyone. The thousands of staff needed are not available, and the delay to travellers would cause howls of outrage. Even pre-Schengen, there were lots of back roads, footpaths etc. that only local residents were authorised to use.
Yes, they can add extra checks at airports, but the airlines already have details of all passengers, so the info is already available to intelligence services. This meeting is in Sicily, that makes sense, "they" have data on everybody flying in, and it is easy to put checks on the ferries from the Italian mainland. Blanket checks on everyone entering Italy would be a massive and expensive waste of resources.
Conclusion: This should not cause major disruption to travellers entering Italy.