The best way to deal with a petition to the European Parliament? Admit it and then we'll see (C-261/13)

In its Judgment in case Schönberger v Parliament, C-261/13, EU:C:2014:2423, the CJEU has assessed the limits of the right to petition the European Parliament under art 227 TFEU, as informed by art 44 of the EU Charter of Fundamental Rights. In a case that confirms a previous Judgment by the GC [EU:T:2013:111, not available in English], the CJEU has clarified the controls, checks and balances applicable to a rejection of a petition and, maybe more counterintuitively, the lack of controls applicable to the admission of a petition. This may sound absurd and unnecessary, given that there would seem to be no need to control the reasons why the European Parliament admits petitions.
However, the discussion seems to actually not have been about how to control de admission of petitions, but the actions that the European Parliament decides to engage in once the petition is admitted. On this point, and showing a very clear deference for the political process involved in the right to petition, the CJEU has stressed that
it is clear from the provisions of the TFEU and from the rules adopted by the Parliament for the organisation of the right of petition that, where the Parliament takes the view that a petition meets the conditions laid down in Article 227 TFEU, it has a broad discretion, of a political nature, as regards how that petition should be dealt with. It follows that a decision taken in that regard is not amenable to judicial review, regardless of whether, by that decision, the Parliament itself takes the appropriate measures or considers that it is unable to do so and refers the petition to the competent institution or department so that that institution or department may take those measures (C-261/13, para 24, emphasis added).
The question at this point is how to interpret this passage, which seems to either not require any reaction at all from Parliament, or a very minimum 'referral' of the petition to a different institution or department. Ie, in the best case scenario, all the Parliament needs to do is to pass the hot potato onto somebody else. In the worst case, it may just decided that there is nothing that can be done.
The lack of appetite for a control of the actions that follow a petition is understandable. However, an extreme reading of Schönberger v Parliament would simply result in the European Parliament never rejecting any petition in the future (that would be open to judicial review) and instead admitting them and immediately declaring that there is nothing they can do (with, or without further referral). Whether this provides any meaningful effectiveness to art 44 EUCFR and art 227 TFEU is at least debatable. However, there is nothing I can say about this. Hopefully the experts will.