The Richard III Society was hell bent on proving that Richard III was not a hunchback. The discovery of his skeleton did prove that Richard had a badly distorted spine.
Richard III was not definitely not a 'hunchback'. He did however have a badly distorted spine due to a condition known as scoliosis that probably started to develop in his teens and over the course of several years caused a sideways twisting of his spine. When Richard was dressed it would be most unlikely that this distortion would be noticed other that a slight dipping of one of his shoulders that would be barely noticeable given the fashions of the day.
A hunchback appearance is caused by a different condition - hyper-kyphosis, which is an excessive outward curve of the spine, and there was no sign of this in Richard's spine. As far as I'm concerned I think that nothing untoward would have been noticed until after his death when he was stripped naked, slung over the back of a horse, abused and taken to Leicester. Only then would it be noticed that his spine was not straight. From this point onwards the diseased spine would be used as negative propaganda by his enemies.