This question is addressed by several acharonim. R. Jacob Reischer argues that since a kohen who does not perform the blessing is as if he has violated three positive commandments, the Sages said that a safek kohen should do it. And since he is doing it m'd'rabanan, there is no problem with making a beracha:
Shu"t Shevut Yaakov 1:93
אלא ודאי צ"ל אף על גב ...
The answer is Chezkat Chulin (permitted) + Safek if something fell there, lead to permit even for An Isur Deorayta.
The Gemara Yebamot says regarding a berayta similar to our Mishna, that the Kula שאני אומר (because I assume that)
is because of a Rov Chulin (> 50%, not > 100/1). Even if the Teruma falls on the chulin, it's batel berov deorayta. this is ...
In short, the rational is the rules of Chazaka. My answer is based on the Rash Negayim 4.11.
See Nazir 65b
MISHNA: Any case of uncertainty with regard to leprous sores is initially deemed pure until it is established that it is a case of ritual impurity. Once it has been determined to be a case of impurity, uncertainty concerning it is deemed impure. ...
The Rambam Hilchos Korban Pesach 3,2:
באומר לעבדו צא ושחוט עלי וקבע לו ושכח העבד מה אמר לו רבו. והוא שיתן לו רועה של רבו גדי וטלה ויאמר לו שחוט שניהן כדי שתשחוט כמו שאמר לו רבך והרי אחד מהן שלך על מנת שלא יהיה לרבך בו כלום. אם עשה הרועה כך אחר כך יהיה אפשר לעבד להתנות כמו שביארנו
When someone tells his slave to slaughter a Pesach offering and the ...
Rambam writes in Hilchos Melachim (11:1):
...anyone who does not believe in (the Messiah), or one who does not
wait for his arrival - he is not merely denying the other prophets but
rather denies the Torah and Moshe Rabbeinu.
Moreover, the original source for these fundamental beliefs as described by the Rambam come from his introduction to Perek ...