What I think happens a lot is that people use "the Internet is different" as a sort of short-hand for the idea that the Internet should be governed by different underlying principles. But I think it's disingenuous to say that the nature of the Internet dictates that it be governed by different principles. The existing property principles translate just fine.
If they did, we wouldn't be having this conversation. As others have pointed out, physical concepts of scarcity and mutual exclusion are nearly meaningless in the digital realm. Digital systems are capable of acting autonomously as agents; they are not just passive property. Measures to ensure technical exclusion bear no useful resemblance to physical security. Computers give the ability to lay out in machine-readable terms what is "public" and what is not.
Note that I'm not arguing against the right to decide who can access a computer system and for what purposes, only against the use of analogies to physical spaces and existing laws.
An example he gave was seeing a cop drive by your house. Ostensibly that'll put you at ease, the concept that a law enforcement agency is patrolling your neighborhood. Maybe the officer gives a wave, or even chats with you for a bit if you're out washing your car or mowing the lawn. You feel safe.
How would this possibly translate to "cyberspace"? What if the local PD did a regular port scan of your router, or attempted to crack wifis while on their patrol? We allow searches of our belongings when we get on planes, but when our packets go overseas, we very much dislike the idea that someone from the government might be taking a look.
The rules, he went on to say, are simply different, because expectations are different.
I understand that in the State of California it is unlawful to shoot a whale while riding a camel.