Here's what I meant. Sorry for bringing up a Chinese example but I'm pretty ignorant in Tibetan Buddhism.
The three most famous Zen teachers of all time are Bodhidharma, Huineng (the so called 6th patriarch) and Linji (Rinzai in Japanese). They're considered people who attained sudden enlightenment and reached buddhahood. What do we actually know about them that can be historically attested? Almost nothing. What we know is that their stories and teachings are mostly the products of later ages. For instance, the fame of Huineng (who was illiterate according to the story) is primarily because of a monk called Shenhui, who claimed to be the Dharma-heir of Huineng, and was a controversial figure of his time. While some of Shenhui's teachings could survive, in the last 1300 years nobody really cared about those, unlike things attributed to Huineng which were not taught by him at all.
Waiting for a "greatly enlightened master with a rainbow body" is like waiting for Maitreya to come. Actually, the single person respected by all Western Buddhists and many non-Buddhists is His Holiness the Dalai Lama. Indeed, if we look around in Europe and America, Tibetan Buddhism is thriving. On the other hand, Zen and Theravada is doing quite well too, even if they have no universal celebrity.
It sounds good to name a single person responsible for something awesome like establishing Buddhism in a country. But in fact, even Shakyamuni Buddha couldn't make Buddhism a major religion in India single-handedly, so there were his disciples who he sent out to spread the word, and the disciples of disciples, etc., and there was Ashoka, so on and so forth.
"While teachers of the middle way, mind only, transcendent wisdom, mantra, and other schools may have their own assertions, the fulfillment of those intentions is the same. There is not a single thing that is not contained within mind."
(Gampopa to Düsum Khyenpa, in "The First Karmapa", KTD Pub, p254)
“If you recognize the world of appearance and existence as the mind, realize the mind itself as empty, and have no grasping at the superiority of your realizations — this is the ultimate view."
(Chegom Dzongpa, in "The Book of Kadam", Wisdom Pub, p609)