Modern is the key modifier. But between Thailand, Cambodia, and Vietnam I thought there was a lot of border movement over the course of history ?
There was a lot of border movement, but most of this had to do with Cambodia/the Khmer Empire. Essentially, Vietnam and Thailand slowly pushed their way into Cambodia - before the French came, Cambodia was forced to pay tribute to
both Vietnam and Thailand. The southern part of Vietnam was once the eastern part of the Khmer Empire, and parts of eastern Thailand were once part of the western parts of the Khmer Empire. Had the French not colonized the region, and Vietnam and Thailand continued to push in on Cambodia, it's possible Cambodia could have disappeared off the map and then Vietnam and Thailand would have to go into direct confrontation over territory, but otherwise to my knowledge the modern-day countries have no historical overlap... for now.
And are you really saying there was no Chinese influence in Cambodia or Thailand ? Or no parts of Vietnam, modern or otherwise that were not influenced by India ?
I can't say there was none either way, but it was extremely minimal.
The Khmer Empire, for instance, was strongly Hindu for much of its history, before converting to Buddhism. Much of its political, religious, and social structures were heavily influenced by that of India - for instance, Khmer kings were often called "deva-raja", or "god-king," to symbolize their connection with the Hindu deity Shiva. Hindu legends such as that of Rama are still an important source for much of southeast Asian literature and the arts - for instance, many of the puppet plays performed in Indonesia and Malaysia take their stories from these legends. A similar situation occurred throughout much of southeast Asia
except Vietnam before they converted fully to either Buddhism or Islam.
Contrast this with Vietnam which bears an uncanny resemblance to China. Imperial Vietnam used written Chinese as well as Chu Nom - which was essentially Chinese characters with extra, native-invented characters tacked on. They had an imperial examination system pretty much like that of China. The three big Chinese belief systems - Buddhism, Confucianism, and Daoism - were also considered the big three belief systems of Vietnam. Even today, pretty much almost all of Vietnamese technical vocabulary is derived from Chinese - even Indian terms that usually crop up in Buddhist contexts are borrowed from Chinese (that is, the Chinese-translated/transliterated versions of the Indian originals, rather than a direct translation from Indian languages), so even the biggest "Indian" influence in Vietnam, Buddhism, went through a heavily SInicized filter and adaptation.
Ultimately, Vietnam's pretty much the oddball of Southeast Asia. In my opinion, culturally, it should be grouped with East Asia rather than Southeast Asia. While it would be incorrect to say Vietnam was a miniature clone of China culture-wise, as the Vietnamese still kept many of their native customs and ideas, as well as a strong anti-Chinese identity, these ideas had little if anything at all with India.