My one an only contribution to this thread is:
Don’t look to martial artists for historical information.
Unless the martial artists happens to be a researcher or bonafide historian.
There are plenty of verifiable sources in regards to Ch’an, it’s inception and it’s spread.
I give the first word of advice because all too often things are drawn from a single source or word of mouth. BOth of which have not much credibility when it comes to regarding it as a fact.
The general practice is to attempt to gain the information from at least 3 unrealetd and uneffected sources.
Confucian, Taoist and Buddhist thought are all intricately woven together in Chinese History. There are buddhist temples which still possess scrolls and records and there is a fairly rich and robust history of China that is available for research. THis research is far apart from the musing of martial artists and the ubiquitos TaMo stories we all here. most of the time the recollection is wrong because it is poorly recollected or incorrectly recollected or just parroted from 100 other sources that are parroting the same thing.
If you say a lie to yourself enough times, ytou just might wind up believing it after all.
So, you can legitimately trace the roots of Ch’an not to TaMo, but to his first disciple Hui ke. THe others that came after Hui ke are pretty well defined historically speaking up to the 5th and 6th patriarchs where there are some misgivings as to which was which and who was the legitimate patriarch of Ch’an.
As for Shaolin, well, the building has been repaired, but there it is, the whole schamoley just sitting there, being all temply in Henan province just a short trip from Luoyang.
While the PRC may have stemmed some info, they didn’t stem it all and there are records and history of China that go back as far as when europeans were stiull crawling out of caves and sniffing each others bums. 
Anyway, Kungfu is not martial arts, it is a modern blanket reference term for chinese martial arts, but in actuality it is a misnomer. The idea behind attaining Kungfu comes through the morals and ethics as taught in the treatises and lectures of Confuscious (Kung Fu tze). The rules for living established by Kungfutze were ingrained into the social more of the chinese empire for 600 years or more before Buddhism became popular in China. The Dhyana were practiced in China long before 520ad (the alleged arrival of the monk Bodhidharma) and Chan and Zen were founded and developed at Shaolin Temple in Henan. THis is the originating place of Zen for the whole world.
The Shaolin Temple also, like any other buddhist temple was a politically active place. People gathered at temple to get their religion, but also for the sangha (community) and they would get their instructions for living a better life from teh priests and monbks. Ergo:the temples were political places because the advice given had to fall in line with the Government pov or the temple would be treading on thin ice.
Anyway, there is a ton of information out there. Just don’t look for too much of it from Kungfu teachers. Sure, some of it’s there, but it is not the most reliable source for information about history.
cheers