Samírien is an Early Quenya (i.e. Qenya) name from Tolkien's earliest ideas on his Legendarium and its languages (from 1910~). Its elements are: EQ intensive-prefix sa-, and the gerund of the EQ verb miri- "to smile", with no ties to Valarin, as Tolkien had not yet devised it at the time. And this "Sagamirâyen" does not resemble any Valarin word, while it is also quite unlikely that the Elves would adopt an affix from a Valarin word, let alone use it in other expressions (indeed, there were other words beside Samírien that employed sa-. Are all of them Valarin in origin, then?).
More importantly, Samírien became gibberish as early as 1930~ when Tolkien updated his approach to the languages drastically, and √MIRI (the Primitive Quenderin root of EQ "to smile") became √MIR "precious", with its well-established derivations like mírë "jewel" & mírëa "jeweled" as opposed to EQ mírea "smiling". In other words, if you accept MIR to mean "precious, treasure, jewel, etc.", then you cannot use it also for "smiling", since doing so would be quite a big logic gap. Similarly, Nost-na-Lothion is a name from Gnomish/Goldogrin, which is Sindarin's first draft around the same time with Samírien, and it also became quite meaningless after 1930~.
And Lúthien would say that an imagined thing could just as well offer the truth. I could tell you a completely made up story with a profound moral of which to learn. In her case, her experience led her to a piece of music which I can easily believe to be of Elvish origin. And yet it is imagined! Then we must realise, her experience's being truth or fantasy matters little. Indeed, what matters is that it is beautiful even if it is not "real". I thank you both for this lesson on the in/significance of "truth" or "reality".