The gemara (Nedarim 11a) tells us that whether a neder of "lo chulin she'ochel lach" ("what I eat of your is not chulin") is valid depends on whether you hold michlal lav atah shomea hein. The Mishna in Kiddishin (61) writes that Rabbi Meir learned from our parsha that when a tnei is made the condition must stipulate both the positive and negative consequences of its bring fulfilled. Moshe Rabeinu told the Bnei Reuvain and Gad that if they help in the conquest of Eretz Yisrael they will receive land on the west bank (positive); if they don't help in the conquest, they will not receive the west bank portion (negative). R' Yehudah disagrees and holds that implicit in the positive (if you go, you get what you want) is the converse negative consequence (if you don't go, you don't get what you want) -- it need not be formally articulated for a tnei to be work. Here too with respect to Nedarim, according to R' Yehudah "not like chulin" (not chulin) implies the opposite, "like hekdesh", while according to Rabbi Meir it does not.
All the seforim of the Roshei Yeshiva ask the same basic question on this gemara. If a person stipulates "If X is true you get Y", obviously his meaning is that "If X is not true then you don't get Y." The only reason Rabbi Meir holds that the converse must be spelled out when making a tnei is because tnei must conform to the exact specifications set down in our parsha. The meaning may be clear without the extra verbiage, but according to R' Meir tnei must follow a specific technical formula. But what does that formula derived from the parsha of tnei have to do with the topic of nedarim? Just because there is a formula the Torah sets down for tnei (even when meaning is otherwise clear) does not mean that formula must be adhered to with respect to nedarim or other areas of halacha!
The answer in a nutshell is that the common denominator between tnei and nedarim is that both require explicit speech. "Ish ki yafli lindor neder" -- hafla'ah means to articulate, to express in a clear form. It's not enough for the words of a neder to imply a certain meaning -- they must clearly express what is intended. The reason tnei requires such an elaborate formula according to R' Meir is that although the meaning is otherwise understood, the words must still explicitly and clearly state what is intended. Michlal lav atah shomea hein is not a halacha in da'as, but it is a halacha in dibur.