They are. Rugby gets significantly fewer head injuries and those that occur are less severe. The perceived safety leading to greater risks and injury is a well-documented phenomenon, not just with football.
I don't disagree at all, and I think some of this can be seen by examining why the United States is the defending Olympic rugby champion--since 1924.
Here is a description of how it happened, but my summary is all you really need.
The USA had legitimately won the gold medal in 1920, but the sport had been abandoned in the country almost immediately. When 1924 rolled around, the country had no active rugby players. The games were to be held in France, and the French rugby team was confident they would win easily. Part of the reason, surprisingly, was the ugly rowdiness of their fans--the English team refused to play because of them. The French demanded that the USA produce a team so they could dethrone the defending champions, and the USA produced a team with a few of the people from the last team, people who had not played the game since. The rest of the team was made up of football players who had never played rugby.
After limited training, including in England where they learned the basics of the game, they went to Paris to play. As the game went on, the French (who clearly hated Americans) were winning, and they were playing dirty as well. The American football players decided to stop playing like rugby players and start playing like football players, using low, hard, driving tackles rather then the upper body wrestling tackles used in rugby. They injured the dirtiest of the French players this way, and they won the game and the gold medal.
The Americans are the reigning champions now because rugby was dropped from the olympics after that. Various reasons were given, but many sports historians were afraid that the tactics by which a group of football players who had barely ever seen a rugby match, let alone play in one, could win the Olympic gold medal would become the norm for the game.
It is not just the equipment. There is a gentleman's agreement as to how the game should be played, even if playing it differently might be more effective.
Another example, BTW, is shin guards in soccer. Before shin guards became the norm, there was a gentleman's agreement not to use tackling techniques that could potentially injure a player. With mandatory shin guards, that gentleman's agreement became a relic of the past.