I would class "chav" as being beyond the bounds for the sake of being beyond the bounds. Like 19" wheels on a Honda civic with rubber bands for tyres, handling gone, comfort gone but they look mean. Now if it's a show car fair dues, but for a road car......does not have to be physical bounds alone, it can be the bounds of general taste or just simply cheap and nasty (see: Halfords "styling" section)
Simpler definition might be adding something for glitter rather than style. e.g neons matching facia dial lamp colours in the footwells giving a glow with courtesy lights at night = style, same neons permanently illuminated and pulsating to the sound of house music = chav. Show car with neons underneath for photshoot = style, drive it down main street with the neons = chav.
Just my tuppence worth.
I can see your point and agree to an extent...but I do think that the term 'chav' is thrown around a little too easily lately.
For instance, that rear spoiler on your 156 does pretty much nothing other than stop you seeing out of the back window....and it can be bought from the styling section at Halfords (honestly, my Wife is the manager of the styling section at Halfords...they may have utter tat on show but if you were to look at what they have in stock or can order you would be very very suprised at both the range of stuff and the prices!)....what I am trying to say is that, with how some people define chav, your spoiler fits into the description you gave above.
Now, dont get me wrong as I love the big 156 spoiler and actually requested it fitting to my 156 before I would buy it, but what is wrong with wanting a mean looking car and doing things to it to personalise it in a few little ways if you are willing to lose a bit of the practicality? It's your car after all so if you can live with that practicality then so be it.
My personal definition of a chav car would not be a 147 with large wheels or a GT with chrome wing mirrors...it would be an old base model Saxo or Corsa with every concievable peice of stick on tat thrown at it such as big aluminium wings stuck on the roof, headlamp eyebrows, a 10" exhaust that is hanging from the back bumper out of a hacksawed wobbly hole, partial mirror window tints on the back windows, M3 style mirrors but without the custom base plates, Fast and the Furious graphics over the top of the standard paintwork and fake BMW wing vents.....the list goes on but that is what I would define as Chav. There has been no carefull reasoning to what they have done and have simply thrown everything at the car...not one or two tasteful things...just everything.