According to Rambam (Hilkhot Milah 3:7), not only is it permissible for a gentile to circumcise himself, it is a mitsvah!
As he writes in a responsum (ed. Blau # 148), this is in the category of eino metsuveh v'oseh; one who performs a mitsvah in which he is not obligated:
מותר לישראל למול הגוי אם רוצה הגוי לכרות הערלה ולהסירה, לפי שכל מצוה, שהגוי עושה, נותנין לו עליה שכר, אבל אינו כמי שהוא מצווה ועושה
It is permissible for a Jew to circumcise a gentile...since [for] every mitsvah that a gentle does, he is given reward, but not [to the same degree] as one who is commanded and does it.
However, R. Pinhas Horowitz writes in Panim Yafot (Genesis 17:1) that Abraham didn't circumcise himself before being commanded to, since it is forbidden for even a gentile to wound himself.
This is somewhat similar to the answer given by R. Yehoshua ibn Shu'aib (quoted here), but the latter notably does not state that there is an actual prohibition.
Importantly, however, the claim that a non-Jew may not injure himself is quite dubious. See R. Pinchas Zvichi's lengthy responsum in Ateret Paz (1:3:HM Ha'arot 7:3) who questions this.
Furthermore, not every injury is included under the rubric of "wounding". I am not aware, for example, of any sources the prohibit ear piercing for this reason. (R. Yitshak Yosef writes explicitly that it is permitted in Yalkut Yosef YD 182:11). It seems very reasonable to assume that if one has some reason to perform a circumcision, (a procedure whose merits can be argued (at least in certain cases) on health grounds) that it wouldn't be considered a wound at least for a Jew. The parameters of wounding for a non-Jew may or may not be identical. It is difficult to know, since almost no sources indicate that it exists at all).
In summary, the answer to:
Is this his rhetoric, or is this discussed anywhere in Jewish literature?
In the main elements of the question: that non-Jews are prohibited from injuring themselves and that circumcision counts as a forbidden injury are indeed found in Jewish literature. However both points appear to be minority views. Whether or not referencing an obscure writer and ignoring the views of classical writers can be considered "rhetoric" is up to you to decide.