Ok... I think it became rough in the 1800s
From memory i thought there was some disagreement about it as well... Iv gone to google to confirm it all and this is what wiki says...
The Reverend William Webb Ellis (24 November 1806 – 24 January 1872) was an English Anglican clergyman and the supposed inventor of rugby football while a pupil at Rugby School. According to legend, Webb Ellis picked up the ball and ran with it during a school football match in 1823, thus creating the "rugby" style of play. Although the story has become firmly entrenched in the sport's folklore, it is not supported by substantive evidence, and is discounted by most rugby historians as an origin myth.
The William Webb Ellis Cup is presented to the winners of the Rugby World Cup.
It goes on to say
The sole source of the story of Webb Ellis picking up the ball originates with one Matthew Bloxam, a local antiquarian and former pupil of Rugby.[2] On 10 October 1876,[11] he wrote to The Meteor, the Rugby School magazine, that he had learnt from an unnamed source that the change from a kicking game to a handling game had "...originated with a town boy or foundationer of the name of Ellis, Webb Ellis".
On 22 December 1880,[11] in another letter to The Meteor, Bloxam elaborates on the story:
A boy of the name Ellis – William Webb Ellis – a town boy and a foundationer, ... whilst playing Bigside at football in that half-year [1823], caught the ball in his arms. This being so, according to the then rules, he ought to have retired back as far as he pleased, without parting with the ball, for the combatants on the opposite side could only advance to the spot where he had caught the ball, and were unable to rush forward till he had either punted it or had placed it for some one else to kick, for it was by means of these placed kicks that most of the goals were in those days kicked, but the moment the ball touched the ground the opposite side might rush on. Ellis, for the first time, disregarded this rule, and on catching the ball, instead of retiring backwards, rushed forwards with the ball in his hands towards the opposite goal, with what result as to the game I know not, neither do I know how this infringement of a well-known rule was followed up, or when it became, as it is now, a standing rule.
Bloxam's first account differed from his second one four years later. In his first letter, in 1876, Bloxham claimed that Webb Ellis committed the act in 1824, a time by which Webb Ellis had left Rugby.[11] In his second letter, in 1880, Bloxham put the year as 1823.
The claim that Webb Ellis invented the game did not surface until four years after his death, and doubts have been raised about the story since 1895, when the Old Rugbeian Society first investigated it. The sub-committee conducting the investigation was "unable to procure any first hand evidence of the occurrence"
So its become a bit of a legend...
Your explanation matches the original account very well so iv given you the points...
