I used to attend that church for many years and I know the persons involved (except the Bishop-I knew of his predecessor but not him). There are basically two views from the Greek (oh yes! They ARE Greek -- I will explain at the end of this post) Orthodox side. The first is that this is about jurisdiction due to the order mandated by Orthodox tradition. i.e., if there emerges a situation where there are two bishops in one ... diocese/region/area/whatever, then this makes out the Orthodox claims of unity under one God and one bishop inaccurate. Well, we all know how that theme went. Nektarios himself says that there are indeed areas like the USA and Australia etc where there are different bishops (he fails to mention that that is exactly due to the demands of people for their own language and culture, however traditional this may be or not) but that is "a problem." He will not, of course, dare say that these other areas are schismatic or heretic because, well, he will have a lot to answer for to the Ecumenical patriarchate. The other view is that one of the Russian (or Canadian / Russian or, basically, non-Greek) priests acted in a deceiful manner, failing to come to the liturgy and proskomidi on time in order not to commemorate Nektarios, as the Greek priest must do in that Church, other accomplices handing out petitions to (presumably Russian?) members of the Greek-dependent congregation to join the new, Russian one, etc.
First, I do not see any mischief there because I do not think that the Russian priest would have to keep coming late in order to maintain consistency between cocelebrating liturgy AND not commemorating the Greek Bishop. I suspect that anyone who is THAT detail-orientated and wishes to avoid doing something that goes against the proper order (like wanting to start a church under another bishop and therefore avoiding to commemorate the current one) would see that the rest of the liturgy is still understood as under the blessings of the current bishop. Thus, cocelebrating in such a liturgy does not let someone off the hook just because that someone escaped the first few minutes of the proceedings where the current Bishop's commemoration was taking place. Simply put, if Kyril (the Russian guy) was trying to avoid anything that entailed accepting the current (Greek) Bishop's authority, he would have simply NOT cocelebrated in that church. I cannot see why he would not have been able to just contact the members of the Greek-rependent Church outside liturgy times and announce the beginning of the Russian parish. As, in fact, this seems to have happened, according to the same people who complained against the Russian initiatives, by the Russian entourage (non-priestly, not partaking or anything, but just being there with the congregation) who were in fact getting people to sign the petition for a Russian church.
Now, with regard to how Greek that church is, there is a lot to be said, but I will skip all the gossip and I will just concentrate on the facts which are easily found. The Patriarchate may be under the jurisdiction of the Ecumenical throne in Istanbul but the money comes straight from very conservative and very (but VERY) nationalistic Greek sources. I am not providing here any details because these thiongs are not exactl;y unknown, and because well, I am not sure if anyone is interested. If asked, I will, however, offer proof (it's all over the internet anyway, by the admission of the Greek priest himself).