The entire answer that you have linked to is a pastiche of outright misinformation (such as the claim that Eastern Jews shunned hygiene) or carefully chosen half-truths (like the newspaper article declaring that "Judea" is at war with Germany). Taken as a whole, it amounts to a blatant example of Holocaust denial, and one that can only be maintained if you assert that everything written by every historian on the subject is just propaganda, but everything written by the Reichsminister of Propaganda somehow wasn't.
To respond directly to your questions:
Did the Nazis try to explain Kristallnacht as the peoples' revenge for this murder?
Yes they did - and not just as revenge for the murder of vom Rath, but as revenge in general for the systematic enslavement of the German people to the will of some international Jewish conspiracy. Every feature of the Weimar Republic that had preceded the Nazi rise to power was linked in the popular imagination with their defeat at the end of the Great War, and was seen by far-right conspiracists to be evidence of Jewish control. All of the discrimination foisted on Germany's Jewish communities was understood as retaliatory, and the death of vom Rath provided a perfect opportunity for a pogrom.
The manner in which vom Rath - a third secretary - was hastily promoted several steps up the diplomatic ladder demonstrates the extent to which, for political reasons, his death needed to be symbolic. This was not just an act of retaliation by a lone Polish Jew for the suffering of his parents; this was now representative of Jewish opposition to Germany. As such, the incarceration of Grynszpan would only be treating the symptom: Germany needed to respond to the cause.
Was there any evidence, that Kristallnacht had any kind of "grass roots" motivation and was not entirely state sponsored event?
No, there isn't. The NSDAP presented "Kristallnacht" as an eruption of popular anti-Jewish sentiment, but this claim was patently false - and falsifiable even as it was being made. Germany played host to an enormous number of foreign journalists who reported on the violence even as it was unfolding, and as chaotic as individual acts of vandalism were, there was an order to the madness. Plain-clothed SA officers encouraged popular expressions of anger while the police (having been instructed to stand back) watched on.
In some instances, police stepped forward and tried to break up the hooliganism, but this was evidence of the sloppiness with which the entire event had been coordinated. Hastily put together as it was, there was insufficient time to get the message out, and some police departments were issued with contradictory instructions. Fire departments needed to be at the ready in case the fires spread, but were also told not to put out burning synagogues. Nonetheless, some fire fighters chose to disregard those orders.
Martin Gilbert (Kristallnacht: Prelude to Destruction, 2006) provides a number of examples of police officers and fire fighters who sought to assist the embattled Jews, as well as some instances of civilian assistance given to the victims. By and large, while the event was an unpopular one, most people still felt that Jews posed an existential threat and that this threat required a solution. They just wanted one that was neither so violent, so costly nor so terribly messy.
Anthony Read and David Fisher (Kristallnacht: The Beginning of the Holocaust, 1989) provide a very comprehensive overview of the events leading up to the November pogrom, the execution of the event and its aftermath - as does Saul Friedlander (Nazi Germany and the Jews: The Years of Persecution, 1933-1939, 1997), pp268ff.
For my money, the best overview can be found in chapter 5 ("Pogrom, 1938-1939") of David Cesarani's Final Solution: The Fate of the Jews, 1933-1949 (2016) - especially from p181 onwards.
