No, they don't. They merely can be converted back to decimal with those numbers of significant digits without loss of information.
That is important because (a) if this matters, you have to make sure you actually control the number of significant digits when converting to decimal, or you might end up with a different decimal, and (b) the operations that you do on the floats do not reliably behave as if there was the supposedly represented decimal number stored in them.
Now, sure, you can use floats for currency, if you know what you are doing, but the point of the warning against it is that you have to know what you are doing, and chances are you don't, or if you do, then you know where you can ignore it anyway.
(That is, unless you mean nothing more than that you can encode the information contained in an n-digit decimal in a float/double--which of course is true, but not particular to floating point numbers, as any state with a certain number of bits can, of course, encode any information of no more than that many bits, somehow.)
Floating Points are hard. There is a study done with academics that shows that even researches that works with float point everyday forget about the format intricacies. And the study didn't even look into the compiler mess.
But I agree with you, some (a lot?) of caution is needed when working with float point is good.