Long time no see probably derives from pidgin English spoken by Native Americans or Chinese immigrants, although no one is completely sure.
It matches the Mandarin Chinese phrase 好久不見 (hǎo jiǔ bú jiàn) word-for-word,* which is grammatical in Mandarin.
When you say long time no see, you are pretending to speak broken English, fitting English words to a foreign or pidgin grammar. The phrase is used so much, many people use it without knowing that, but to native ears, it certainly sounds like pidgin English because of the ungrammaticality you noticed. A few other pidgin phrases have gained some currency in English, such as: look-see, from Chinese pidgin English, as in "I'll have a look-see"; savvy to mean "understand", as in "You savvy?", probably from West African pidgin English; and da kine, Hawaiian pidgin English for "the kind", but meaning pretty much anything, or sometimes "the original kind" or "the best kind". To retain their distinctive character, these phrases don't adapt to English grammar; they retain their own grammar even when included in English sentences. Sometimes people modify long time no see, retaining the pidgin grammar; for example, long time me no see you girl.
*Ignoring the usual subtle differences between corresponding words in different languages.
Yes - You say that, but [some refutation or caveat] is idiomatically commonplace for many native speakers, in response to an assertion they disagree with.
It's nearly always used in a context where although the speaker doesn't fully agree with the preceding assertion, he recognizes that there's some truth in it.
In fact, you'll often hear You could say that, but..., which more explicitly acknowledges that the assertion is at least "credible", even if it's not completely accurate. Note that in this usage, you = one, anybody, not necessarily the person being addressed (i.e. - what it amounts to is something like It wouldn't be ridiculous for you/someone to say that, but it's not entirely true).
Also note that if the personal pronoun is stressed (You say that, but...), the implied meaning shifts significantly. This form almost always occurs in contexts where the speaker completely disagrees; he intends to dismiss your opinion on the grounds that you're ignorant or biased, and/or to cite other sources more authoritative than you to refute what you said.
Best Answer
This means that I have no right to provide an opinion, or that my opinion won't be considered to be important in deciding the issue. The issue is entirely in the hands of others to decide.