Hi.

It even makes a difference if the green (right) arrow is painted or lit:
A lit arrow tells you that you can turn without paying much attention to traffic from other directions, all you have to care about are pedestrians who might have a green (aka "walk") light as well as you.
A painted arrow tells you that you are allowed to turn, but only if the other traffic allows it (you have to stop first). Of course, pedestrians might still be crossing the road you want to turn to, so you also have to watch them.

Personally, I think this is a helpful way of handling right turns on red lights:
You are generally not allowed to turn right on red, except expresssively allowed. The different handling of green light and green paint might be confusing at first, but it still has it advantages to those who plan traffic flow and traffic control as well as for the drivers themselves.

cu,
sven