I don't think it's that Apple can't tell the difference, it's that the cellular networks are inherently insecure. The entire telephone system is an example of "it's insecure, but we can't fix it without breaking compatibility."
It's trivial for hackers and scammers to spoof caller ID information. There are even services out there on the Internet that will call anyone you want and provide caller ID info you specify. It is the same tactic that lets scammers appear to be "local" by copying your area code and prefix. It's a 1 in 10,000 chance within a prefix, but I once got a call that showed up as a friend's number, but was a scammer.
There is a way I could conceive that Apple could actually authenticate their own calls, however. Suppose Apple was making a legit call to you. They could use their existing secure data channel (the one that feeds push notifications) -- NOT SMS! -- to send your phone a secure message which would indicate to the phone "A legitimate call from Apple is going to arrive in the next 30 seconds." The phone doesn't have to display anything in reaction to this, but then when the call does come in, some sort of visual indicator could be used to show that indeed this call was "authorized". In fact, this scheme could be useful for any entity trying to legitimately call someone. Of course Apple would charge a fee for this service to outside entities, but I'm wondering if it's going to come to a point where a system like this is all but necessary.
In theory, the phone system could be reworked to be secure. I think one of the main reasons it isn't being done is because there have been some seriously scary incidents in the past where entire regions of the US were without basic landline phone service for hours or days due to simple misconfigurations or bugs. Since telephone service is regulated, failure to provide service can result in some severe penalties. IIRC, if you were dying and 911 failed to work - especially on a landline - you or your family could sue and likely win. Due to both the fact that it has happened before, and the fact that if it does happen the fines can be astronomical, many entities are afraid to even look at the CO switches the wrong way.