Do untrained assailants/attackers/bad guys exist? Absolutely, and I think you'll find they're actually the vast majority. Head to a prison, and count the numbers of detainees practicing their forms, or ask them their opinion of "martial artists" as opponents. There's not really much doubt about it, when it all comes down.
However, the big problem comes when people start assuming some rather unrealistic things about such attackers. Namely, that untrained equals unskilled, that untrained equals not dangerous, and possibly worst of all, that a response against a trained attacker works just as well, if not better, against a non-trained attacker. In other words, this:
BUT: should always assume it is a Worst Case Scenario: highly trained, highly skilled fighter.
An untrained attacker is different to a trained attacker in their tactics, movements, and responses/reactions. If your training is geared around "highly trained" as a "worst case scenario", and therefore doesn't deal in the realities of an untrained attacker, you may just find that your "worst case scenario" simply isn't.
A trained attacker will be consistent (in the types of attacks they use, the power source used, the angling used, and so on), they will do things that don't sacrifice their balance, which will keep their advance (closing ranges) slower. In fact, they typically won't want to change ranges at all, instead wanting to keep to the range that they are trained in. They will have a "comfort zone", and not want to go outside of that. There will also be "gaps", which are present in every form of training, and can be seen and exploited.
An untrained attacker, though, will be inconsistent. They will be unrefined, leading to less balance, but more "commitment" to injuring you. They will sacrifice balance for more power, which will have them close on you far faster than a "trained" martial artist would. And they will close the distance, even if it's not something they intend, with the range changing far faster than most realize. They won't be concerned with a "comfort zone", as they won't really have thought much about their "approach" to combat, instead just knowing that if they hit you so much and so fast that you don't get a chance to retaliate, that's a good thing. The "gaps" that are there will be much harder to see against all the other unrefined actions they are using. There will also be a much greater chance that they have some advantage that is very difficult to overcome, whether it is drugs, alcohol, friends, experience at hurting people, a weapon, or just plain good old fashioned brawn. After all, they're not going to attack if they think it's a fair fight, now, are they?
When you learn a martial art, you are learning to deal with a trained attack. There's really no getting around that, as your attackers are your fellow students, trained in the same system you are. And many systems use their own techniques as the "attacking" methods... which is teaching you the attacking methods of that system. And that's great. But it doesn't really tell you how to deal with the person who isn't trained, who doesn't "attack the right way", who doesn't respond to the techniques "correctly", and who does use a defence (or attack) that is very different to what you've experienced so far. So if you're going to even start thinking of your training as dealing in self defence against an attack, you need to come to an understanding of what the "untrained" attackers are actually like. They are not the same as trained attackers, only easier. In some ways they can be far more dangerous... especially to a martial artist who thinks that, because he can deal with a sparring session against people using the same techniques, strategies, tactics, angling, distancing, timing, range, and weapons as themselves, they can take on a real attack.
Honestly, the easiest type of person to go up against is the guy who isn't trained, but watches UFC and thinks he can do it. They will come in with unrefined versions of known attacks, which are easy to deal with. It's the seasoned "street fighter" who couldn't give a damn about that pajama-wearing fruity stuff, or the rolling around on the ground with a guy in his shorts, who you need to be wary of. They'll take your head off before you realize you're in a fight.
None of this is to say that a trained attacker isn't dangerous, just to point out that an untrained one isn't "easier". They're also very dangerous, but it's a different kind of dangerous. Mistaking one for a form of the other can be a very costly mistake.
Oh, and in regards to the quote that started this, from Choki Motobu, such things really should be looked at with a cultural context as well. The types of untrained violence on Okinawa in the late 19th and early 20th Century wouldn't bear much resemblance to the forms of assaults and attacks found in a 21st Century Western culture, such as the US, or Australia. And even between those two countries, there can be some pretty big gaps as well.
I also think that until we know otherwise, its always best to assume that everyone is trained. I think a LEO would be foolish to assume that the guy he stopped is unarmed. You just never know, so why not take the precautions?
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