I think it's too late for that kind of prescriptivism. "Internet" is not a technical term anymore; it's within the top 1,500 words of the English language according to [1], and its meaning is subject to evolution like any other word. Almost everyone knows it, and almost no one would use it to refer to private networks linked between multiple physical sites (say, SIPRnet, or a CDN's network, as considered separately from the larger network it's embedded into) - including experienced engineers, unless they were being pedantic. At some point the original definition is no more meaningful than an insistence that "data" should be plural, or to never split an infinitive.
> Sun should be capitalized when referring to the star at the center of our solar system, as opposed to other suns -- the stars at the center of other planetary systems.
"Telephone" and "radio" are not proper nouns in your examples, unlike "the Internet," which refers to a specific internetwork. When using "internet" as a common noun to refer to any other internetwork, you should not capitalize according to the rules of English grammar.
This style guide proposes an exception to grammar rules to fit common usage.
I consider it a proper noun because it fits the definition of a proper noun. In your sentence, "the world" is also a proper noun, but you didn't capitalize it for reasons of style, like the sun or the moon. To quote the AP style guide, "AP capitalizes the proper names of planets, including Earth, stars, constellations, etc., but lowercases sun and moon."
The Internet is unlike radio and telephone. Radios and telephones are devices, you usually refer to the one you have nearby. The Internet is a specific global network - this word refers to the same single entity, unlike "telephone" and "radio".
I was 100% for the capitalization of internet until I read your comment.
I think you just wrecked the analogy without realizing it. Your telephone is connected to a telephone network, which is an interconnected network of telephonic devices. Your device is one of many, and has no distinction from others except that it has a unique address in physical space and additionally has an address on the telephone network. Your radio picks up radio signals, a form of wireless mesh network throughout the world (add in signal repeaters used for trunking systems, etc), and you access it with your radio.
In either case of common usage of devices we use to communicate, we don't capitalize the networks, nor do we capitalize the devices (usually, though walkie-talkie I've seen capitalized sometimes).
You use a computer (maybe even the computer - still lowercase - if you have only one in your home) to access the interconnected network of computers to which it is designed to connect via some network adapter and routing device, possibly with a signal modulator/demodulator in there somewhere).
That interconnected network of computers is no different from the interconnected network of radio signals used by trunking systems all over the world, or the interconnected network of telephone signals a POTS line brings to your home.
I think it depends on the network - some have names (like the Internet, ARPANet, DoD's NIPRNet, etc) and some don't (like the global POTS network). Saying "we talked on the phone" is more like saying "we talked on the computer" than "we talked on the Internet."
That's what I was taught as well, but it seems that that's precisely the usage that the new style guidelines are changing. I don't personally think there's anything wrong either way, although my personal sense of style leans me towards the traditional capitalization.
However, one can create other internets, and those are not capitalized.