amstu

I don't know anything about your program or field, so this question may not be helpful: Is a writing sample submitted as part of your application and how much does your field value writing? Is it the expectation of the program that a piece of publishable policy will be produced? 
I ask because, in my mind, spending any extra time on bolstering a writing sample seems much more sensible--provided its a field where that is valued. If this were my field, I would skip the expensive course and pour all my time, energy and research (if applicable) on writing, revising and, polishing. 

I have a similar mentor. Its kind of his schtick. This doesn't sound like a terribly big ethical breach (if at all: maybe administrative breach?) but I think valuing your own internal boundaries is more important at this point than anything else. Politely standing your ground now or disengaging from it, may make a harder ethical ask down the road a lot less emotionally involved. If networking at this event is important to you then pay the entrance fee and attend. 

@KittyCat_PhD, going forward, you will benefit from establishing boundaries early on. You will need to develop tactics that allow you to walk the delicate balance between what you're being asked to do and what you think is the right thing to do.
IRT your current situation, I recommend that you ask yourself "what's at stake?" On the one hand, your advisor wants you to do something that saves (someone) money and (maybe) advances his personal agenda of tweaking his nose at authority from time to time. On the other hand, you are concerned about managing your risk--what happens if you get found out. Potential diagnostic questions include, how would you feel about his request if there were no risk of the ruse being discovered? (Do you not want to do it because you might get caught, or do you not want to do it because it's wrong or do you not want to do it because there's an expanding pattern of rule bending and you want to get off that train?)  Depending on how you answer the question you could put a dollar amount on the price of compromising. 
"Nothing to worry about." You're being too uptight. To me, those are warning flags that this guy doesn't really give a fuck about you. At all. YMMV.

You're going to have to be more specific.

Way, way, WAY more specific.
 

FWIW, I agree with F_L and take it a bit further. You're likely being told that you specifically will not be offered admission without improving your Arabic.
IRT the portion of your OP that I've quoted, I very strongly advise you to avoid the path of  finding the weirdness when you're given a point blank answer.
Here's why. The students you describe may be the reason for the POI's response or they may be exceptions to the rule or they may be the beneficiaries of the benefit of the doubt. Without specific knowledge about their circumstances, dwelling on the inconsistency isn't the best use of your time and you can develop a reputation for being a barracks lawyer.
In the strongest possible terms, I recommend not pursuing this course of action.
I recommend that you thank her for her thoughtful reply and that you're going to take her guidance to heart (if you intend to do so). If you're still going to apply, simply thank her for her reply.

Hey, @mk-8! You've got this ? I don't feel like I've gotten a ton accomplished either, but I'm gonna try and start fresh and prioritize my time. I'm trying to look at it not so much of what I haven't accomplished in my working part-time/being lazy but the opportunity I have to turn it around.
My goal was to do a bunch of thesis stuff this summer, but now I'm starting to realize that my conference presentations and PhD apps come sooner, so I may need to reorient myself. I haven't done nearly enough reading, but that's okay. My chair just has very lofty goals for me and will have to understand what else I have going on. 
And @verjus, accountability is truly key and very important! 
I'm wondering if anyone wants to set up a pm chat where we can share our plans/goals and report back to each other every so often? I'd totally be down for that