כופר בתורה שבעל פה does not mean that he denies the theoretical existence of any תורה שבע"פ but that he denies the actual תורה שבע"פ in our possession--so if someone denies the authentic תורה שבע"פ he would fall under that category. Furthermore, such a person would be included under the category of מכחיש מגידיה as someone who denies the reliability of the bearers of our tradition (Rambam, Hil. Teshuvah 3:8).
However, Rashi in Shabbat 31a explains the case of the gentile who came to Hillel to convert and said he did not accept the Oral Law:
שלא היה כופר בתורה שבעל פה אלא שלא היה מאמין שהיא מפי הגבורה. R. Moshe Feinstein (Dibberot Moshe, Yevamot, p. 477; Iggerot Moshe, vol. 9, YD 41:2) explains Rashi's comment to mean that the potential convert did not believe that what Hillel was teaching him was part of the actual Oral Law transmitted by God, but did believe in the existence of such an Oral Law. According to R. Moshe's interpretation of Rashi, it is possible that such a person would not be considered a heretic.