You are correct, I can not find where arbitration is forbidden in the directive also it is quite the opposite.
I think in this particular case we are talking about Directive 2011/83/EU of the European Parliament and of the Council on consumer rights.
Article 6(1)
(t) where applicable, the possibility of having recourse to an out-of-court complaint and redress mechanism, to which the trader is subject, and the methods for having access to it.
ADR is not forbidden. But it is regulated by 2013/11/EU [1]. In particular:
"
(43)
An agreement between a consumer and a trader to submit complaints to an ADR entity should not be binding on the consumer if it was concluded before the dispute has materialised and if it has the effect of depriving the consumer of his right to bring an action before the courts for the settlement of the dispute. Furthermore, in ADR procedures which aim at resolving the dispute by imposing a solution, the solution imposed should be binding on the parties only if they were informed of its binding nature in advance and specifically accepted this. Specific acceptance by the trader should not be required if national rules provide that such solutions are binding on traders."
I think in this particular case we are talking about Directive 2011/83/EU of the European Parliament and of the Council on consumer rights.
Article 6(1)
(t) where applicable, the possibility of having recourse to an out-of-court complaint and redress mechanism, to which the trader is subject, and the methods for having access to it.