1. This is an example of what the Gemara calls "Shev v'Al Ta'aseh Sha'ani" (see Berachos 20a); that is, it is different when one does not do something actively, but only passively.

2. The Aruch (by Rabeinu Nasan of Rome, who lived shortly before Rashi), in entry "Shev," cites Rabeinu Chananel who explains this idea. What he writes provides an answer to your question. Rabeinu Chananel explains that Hash-m does not punish a person who made himself Tamei and therefore was unable to bring the Korban Pesach. Rather, He gave Kares to a person who was Tahor and was not far away from the Beis ha'Mikdash and yet willfully failed to bring the Korban Pesach. One who made himself Tamei failed to bring the Korban Pesach only in an indirect way, and thus he may bring it on Pesach Sheni. This is considered "Shev v'Al Ta'aseh" and is a lighter form of transgression.

3. A similar idea is stated by Tosfos in Pesachim (93a, DH Ela). Tosfos writes that one cannot say that a person who deliberately distanced himself from the Beis ha'Mikdash is Chayav Kares. Tosfos also writes that a person who made himself Tamei is exempt from Kares.

4. It seems to me that there is no contradiction to the above from the Gemara in Pesachim (69b) that a Tamei person (on Erev Pesach; see Rashi DH Arel) who was capable of making himself Tahor but did not do so is Chayav Kares. This is because the Tamei person who could have become Tahor is just the same as every other Tahor person who -- if he is too lazy to bring the Korban on Erev Pesach -- is Chayav Kares for not bringing it. We do not say that this is also a case of "Shev v'Al Ta'aseh" and he should not be punished since he committed no active transgression, because this is the very nature of the Mitzvah of Korban Pesach; the Torah requires a person to do a positive action, and one who fails to do this positive action is Chayav Kares. If a person is Tamei on Erev Pesach but capable of becoming Tahor, then the act of becoming Tahor is just one part of the process of bringing the Korban. In contrast, a person who was Tahor on Erev Pesach and then deliberately made himself Tamei before nightfall on the 15th of Nisan has prevented himself from bringing the Korban Pesach merely in an indirect manner. This is because when the latest possible time for bringing the Korban arrives it is now impossible for him to do so because of his Tum'ah.

5. However, even though the person who is Metamei himself on Erev Pesach is exempt from Kares, he nevertheless is not permitted to do this l'Chatchilah because by doing so he makes himself exempt from the Mitzvah of Korban Pesach, which the Torah wants every Tahor person to bring. This can be learned from the words of Rabeinu Chananel who said that "Shev v'Al Ta'aseh" is less severe and is not Chayav Kares; this implies that it is not permitted l'Chatchilah. (See Teshuvas Beis She'arim Orach Chaim #369, DH Amnam, Teshuvos Mishneh Halachos 16:86, and Teshuvos Avnei Nezer Orach Chaim 382:2 and Even ha'Ezer 20:8.)

Kol Tuv,

Dovid Bloom