The simplest explanation for what this rabbi was saying is that he assumes that shittuf is prohibited; therefore when Tosafos says that בני נח לא הוזהרו על השיתוף what that means is that in the context of a שבועה there is no prohibition for the ב"נ to mention another being, but there is still a prohibition to worship another being. However, according to those acharonim who understand Tosafos broadly, this would obviously include worship--since the whole discussion is about Christianity.
Alternatively, I would suggest that the rabbi in question was making a different distinction between two types of shittuf, following R. Yaakov Emden in She'eilas Yaavetz 1:41. R. Yaakov Emden distinguishes between belief in multiple gods which are viewed as equal vs. belief in one supreme God “combined” with worship of lower beings. According to R. Yaakov Emden, the former is considered idolatry even for gentiles whereas the latter is permitted for gentiles. [See also Mor u-ketziah, ed. A. Bombach (Jerusalem, 1996), sec. 224, p. 267 and notes there.]