I’m not sure that is totally true. Perhaps it is a matter of what you mean by “dictate”. I believe that the Cardinal did affirm that the diocesan bishop could determine the posture at both times mentioned above…" the prescription of the Institutio Generalis Missalis Romani, no. 43, is intended, on the one hand, to ensure within broad limits a certain uniformity of posture within the congregation for the various parts of the celebration of Holy Mass…" However, Cardinal Arinze added, "…*on the other hand, to not regulate posture rigidly in such a way that those who wish to kneel or sit would no longer be free. *
Oh, it is totally true.
When the GIRM edition came out, there was an almost immediate uproar.
The GIRM covered 2 distinct points in the Mass.
The first point was the time between the Agnus Dei and Communion. For as long as I can remember (and that is back to 1950), we knelt during the time between the Agnus Dei and Communion, only rising when our bench was the next to step into the line going up to Communion.
However, the GIRM specifically said that the bishop could have everyone stand (that is, continue to stand) rather than kneel down after the end of the Agnus Dei.
In a separate line from that statement, the GIRM appeared to indicate that after each one receives Communion, they were to return to their pew and remain standing until the last person had received. This was different from what everyone was used to.
Cardinal George submitted the dubium, and Cardinal Arinze answered the question asked. The question asked was not about the time between the Agnus Dei and Communion starting; it was specifically about the time after one received and returned to their pew.
And Cardinal Arinze’s answer basically said that Rome did not intend to make a rigid rule at that point in the Mass.
The result has been, at least in the vast majority of parishes I have attended Mass, a return to the prior practice of most people kneeling, some sitting immediately on return, and variances locally as to when they might all sit. I have attended Mass in 5 states since that time; and in only one parish, northeast of Sacramento, have I observed anyone standing after returning to their pew; and there, maybe 20% of the people were standing.
Cardinal Arinze did not affirm the bishops’ right to set posture before Communion, as that was not part of the question. No one was questioning the bishops’ right to do so.
Cardinal Arinze spoke only to the matter of posture after reception of Communion, and did not say whether or not the bishops could mandate it (and the bishops were not mandating it; Rome was, as Rome is the source of the GIRM. It appears to be largely ignored (as I noted, I have only seen it in one parish in California). That is not to say that a bishop might not agree with the GIRM and say it is to be followed; but then, again, the Cardinal said it was not meant to be absolutely binding (and practice everywhere else I have been is that it is completely ignored).
I have yet to see or hear of any bishop stating what posture is to be after Communion. It may be that bishops have told their priests that they (the priests) may ignore the matter; or it may be that without any fanfare or rule making, everyone pretty much got the message of Cardinal Arinze’s answer, and chose not to tell their congregations about that specific part of the rule.
It helps to remember that the GIRM is the General Instruction - that is, it is universal, with possible exceptions for some countries. And in the US, the vast majority, prior to that GIRM edition, knelt after returning to their pew. I can’t speak for what anyone does in other countries, as I have not traveled to any since the edition came out. The question was asked by the US bishops, for the US.