If you set up a sign with a click event - run_command, the command will not be run by the user who clicked the sign, but by the sign itself.

setblock ~ ~1 ~ standing_sign 0 replace {Text1:"{text:\"\",clickEvent:{action:run_command,value:\"setblock ~1 ~ ~ stone\"}}"}

-> if you click the sign, the player should run the command, thus the stone should be place beside the player
-X Instead it runs the command from the perspective of the sign, thus the stone is placed next to the sign

In the screenshot you can see the problem.
Camparison between run_command from book and sign

Tellraw and books with click events + run_command work as assumed, no problems