Don't disagree with anything you said, just a point of clarification.
Wernicke's aphasia is indeed a receptive aphasia, although the degree to which comprehension of speech is impaired is variable. To a provider in the field, however, it may appear that someone with wernicke's is understanding you because they will appear to try to respond to questions and may even repeat some of what you said. This might be recognized by asking them to follow simple commands, but the most prominent symptom will probably be that they speak with profuse, fluent (eg. they can produce speach, they have no motor disorder, though the speech may not be intelligible), grammatical, but nonsensical language ("word salad") using inappropriate or even made-up words made of properly pronounced word fragments.
Broca's patients
may be able to produce speech but with a loss of grammar, but the more typical presentation would be extreme word-searching and issues generating words. They may speak in single (appropriate) words with long pauses between. E.g Q: "what sort of health history do you have?" A: uh....head......stroke......brain......years.....two
They may also have problems forming word. Broca's can be thought of as a motor disorder - these patients have a problem generating the motor output necessary to generate speech as well as having grammatical problems. E.g. broca's first patient with this sort of aphasia was called "Tan," as that was the only word he was able to produce.
Side note: often these patients can sing even if they cannot speak - different areas control the motor output for singing (Ozzy osbourne is an OK example of this). They can probably still understand speech, although they may have issues with word order (E.G. misinterpreting "the man bit the dog" as "the dog bit the man"). I don't know if there are any broca's patients who sing to communicate...would be interesting to see a patient who only sings to you.
There are some good videos on YouTube with examples of various forms of aphasia.
In EMS you certianly don't need to be able to diagnose the various aphasias....speech science types go to school for a long time to do that...but it is important to be able to recognize the various presentations that are signs of a possible stroke. I'd dare to say probably more common for these symptoms to overlap than to have a more "pure" type of aphasia.
For more - I like this set of descriptions...not so technical that an EMS provider would get lost.
http://brainmind.com/Aphasia33.html