The Mishna (Nazir 11a) says that a person cannot become a nazir on condition that he can drink wine or become tamei because that would be masneh al mah she'kasuv batorah, creating a condition that violates halacha, as it undermines the definition of nazir which the Torah formulates. Tosfos asks why the gemara used this reason to reject this type of nezirus when there is another reason for rejecting any tnai on nezirus: a tnai can only be made on an action that can be fulfilled through a shliach, as we learn from our parsha. The paradigm for all tnaim is the agreement between Moshe and the bnei Reuvain and Gad giving them land on the west bank on condition that they join in the conquest of the rest of Canaan. Since the distribution of land was done by Yehoshua and not Moshe himself, we learn that a tnai can be made only where an action can be carried out by an agent. Since a person must fulfill his/her own vow of nezirus and cannot appoint a shliach to do so, it would seem that no conditions can be set.
Tosfos answers that nezirus can in fact be fulfilled through shlichus as a nazir can appoint an agent to bring his korbanos to the Mikdash.
R' Akiva Eiger (Shu"T, Mh"K 48) points out that Tosofos' answer works only in the particular case of nezirus, but will not explain many similar cases, e.g. a person can take a neder that he will not bathe ever if (conditionally) he does not bathe today -- there are no korbanos involved in this case, no possibility of fulfilling the neder through an agent, yet a tnai can be made.
R' Akiva Eiger therefore offers a different answer to Tosfos' question. Every tnai in effect undoes an action; if some condition is not met, then action X becomes nullified and negated. Even without the chiddush of a parsha in the Torah to teach us the laws of tnei, we would assume that a verbal condition can negate a verbal declaration -- words can undo words. Obviously a tnai can negate the acceptance of nezirus or the acceptance of a neder. The parsha of tnei in the Torah which includes the criteria of shlichus applies only to actions -- without a parhsa to teach me the chiddush of tnei we would assume words cannot undo deeds. Therefore, only when we speak of making conditions on actions which is a special chiddush of our parsha are we required to meet the criteria of tnei set out in the parsha, including the criteria of being able to fulfill the action through a shlich.
(For a similar approach see this point from the past, and maybe we will also get to the R' Chaim quoted by the Brisker Rav in the beginning of Hil Nezirus, but if not, kareh makom hu lach.)