Why unfortunately? "...times more" asks for doing a rapid multiplication with a subsequent addition, which complicates everything.
Wouldn't that be an argument for simply not using it in front of non-mathematicians rather than to pretend that it means the same as "three times as much" if, and only if, the author intends it that way?
The problem is that, eventually, language tends towards the lowest common denominator unless there's a very good reason for it not to. The LCD here is that they mean the same because, as you point out, figuring the difference is beyond most people. We use language for communication, so even if we have to use completely incorrect terms to get a point across, that's what's necessary.
If a patient has only 10% chance of recovering, and he's visited the next day by his doctor who says, pleased, that he's improved 100% overnight, the patient (if I know patients) will NOT get the message that he still has only a 20% survival chance.