I agree, my understanding of Stoicism leads me to the same conclusion. Epicureans and Stoics seem to have always had a friendly rivalry going on, though they feel a lot like two sides to the same coin. In some ways, to me, Epicureanism is what a Stoic does on their day off.
The rivalry isn't always friendly. If your connotation of epicureanism involves "pleasures of the flesh", it's probably because stoics painted them as hedonists.
