I think the EZY bashing is a bit harsh. Considering they have around 150 aircraft I guess if there's was one or two bad eggs it doesn't make every pilot in the company that way. By the way, was this pilot English? Sometimes things can be lost in translation and what he/she was saying may have been perfectly reasonable in their native language (if you know what I mean).
It's not unusual for pilots to tell the tower that they can accept an immediate departure as this let's the tower know that you won't hang about completing checks, you'll enter and start rolling and it means the tower will perhaps squeeze you into a gap that they otherwise would make you hold for. This allows maximum utilisation of the runway and is good airmanship.
I would think that if the EZY was overly pushy it was because he was on a slot and if you miss your slot the next one is usually in excess of an hour away. If that was the case tho, it would be good for the controller to say to the Helicopter pilot that he had an aircraft on a slot to get away.