The Lubavitcher Rebbe explains in his Haggada (Likkutey Taamim Uminhagim):
The verse regarding the original Korban Pesach (Shemos 12:8) - "ואכלו את הבשר גו' ומצות על מרורים יאכלוהו" (They shall eat the flesh, roasted over the fire, and unleavened cakes; with bitter herbs they shall eat it) would seem to come as a counter-proof to Hillel's opinion that one must bind the Pesach, Matza and Maror together. The Mechilta there deduces from the superfluous word "they shall eat it", that even if one does not have Matza or Maror, he should still eat the Korban Pesach. Thus, the verse is emphasizing how each Mitzva is independent, the opposite to the point Hillel wants to make. Additionally, the simple reading of the verse seems to be (as the Ramban there renders it) that only the Maror needs to be eaten with the Pesach but there is no evidence that the Matza must as well. It is only from the later verse regarding Pesach Sheini that we derive this obligation, which we apply to Pesach Rishon as well.
[He notes at the end that there are those who have an alternate text that substitutes the verse from Pesach Rishon].
Rabbi Menachem Mendel Kasher deals with this question at great length in Torah Shleima (vol. 11 pg. 97-100, and pg. 210-213). From a quick glance through it, it seems as if he tries to prove that the correct text should cite the verse from Pesach Rishon.
One of the Belzer Rebbes (quoted in Hagadas Kol Yehudah) explained that the words "לקיים מה שנאמר" (to fulfill that which is written) are not merely coming to bring Scriptural evidence to the previous statement (for if so it should have used the more common expression "כמו שכתוב" - "as it is written"). It is also a prayer that we should speedily merit to fulfill that which is written with an actual Korban Pesach when Moshiach comes. Being that we already missed the first Korban Pesach, we pray that we should at least make it in time for the Pesach Sheini (and not have to wait a full year), and thus we bring a verse regarding the Pesach Sheini.