I wonder if infringing was the wrong term to use? I suppose this could have depended on what service where you receiving. If I am providing a radar service to a pilot then I have to provide separation from notified areas; commonly 5 miles/1000ft from the published area.
The above is a must for RCS & DC but even if you were on a Traffic Service there is still an obligation on the controller to inform you of traffic that may come into proximity with you, so therefore I would aim to keep you to my prescribed minima.
If you were pootling about on a Basic Service, I would only need to tell you the area is active, it's entirely up to you how close you would get to the boundary. Of course, this leaves you with the possibility of downgrading your service.