I discovered Dunkin Donuts when I moved to New York two and half years ago. Dunkin coffee, IMHO, has superior taste when compared to Starbucks and is slightly cheaper to boot.
Their TV ad campaign touts their product as simple and straight to the point. Small, Medium, and Large. No need for knowledge of any foreign words like "Grande" or "Venti." That language is reserved for the snobby Starbucks crowd.

McDonalds coffee isn't bad either, and it's even cheaper than Dunkin's product. In fact, it's the only reason I would think of stepping into a McDonalds these days (other than asking to use the bathroom, of course).
The new ad campaign for McDonalds coffee is surprisingly / unsurprisingly taking aim at the snobby Starbucks crowd.

Which begs the question - if you are in the coffee market competing head-to-head with Starbucks, do you have to allude to their brand (even indirectly) in your marketing campaign?
I would argue an emphatic "no." Dunkin and McDonalds coffee brands should primarily focus on the virtues of their product, and secondarily on their price points. There's no need to mention the dominant competitor in the space or their "snobby" consumer, even indirectly. Right?
It reminds me of that one Blockbuster Total Access TV commercial, where a direct comparison to Netflix was made. I'm sure Netflix appreciated the free air time:
The first time I saw this, I remember thinking to myself:
"I should really mail that Netflix DVD sitting on my kitchen table."
It didn't even register to me that I had just seen a Blockbuster Total Access commercial.