Unconventional Cover Letter - Trap?

Hey all, 

I've come across a few job applications that request a cover "letter" (they put it in quotes), and is usually followed by something like this:

Your cover “letter” can be a description of your primary creative outlet. Demonstrate your passions. Don't be constrained by conventional ideas of cover letters; choose a style that best suits your needs. Feel free to attach other media as well. Demonstrate your authentic voice.

Is this a trap?  Or do they actually want something out-of-the-box?  Like, if I were super into watercolors (I'm not), should I write about it and upload a picture of a painting?  I can't tell from some of these companies' websites if they're actually looking for more complex people, or if they're weeding out anyone who isn't a "finance bro".

 

Yikes, what kind of jobs do you see these for? If it seems out of place for that type of job, and it’s not your style, I wouldn’t go out of your way to reinvent the wheel.

 

Various positions, usually entry-level, for boutique strategy or management consulting firms.

Right?  It sounds bizarre to me.  No hate on alternative forms of self-expression, but in a job application?  I couldn't tell if I'm old-fashioned or if this is weird.

"In order to make a man covet a thing, it is only necessary to make the thing difficult to attain." ― Dan Ariely
 

I was once asked to share some formative experiences in a cover letter for an IB position and my response was to tell them about the time my college basketball coach told me I was “tough as shit” and had “big balls.” I used those words. I did not get the job

 

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