This seems like the most reasonable (and ethical) reason for the decision. Someone else mentioned ToS, which might be a stronger (but not necessarily ethical) reason. I would think that if it is not a result of the Terms, problems with embedding strongly outweigh the benefits. If it’s just about the Terms, I’d think a good journalist should quote the text in the article (same as reporting on any public statement), then hyperlink the site.
That would fully be compatible with device and accessibility settings, and provide the same verification as the embedded X. It would be better for journalism because editing could happen from the X side in the future, including removal, which is already possible. It would be better for privacy, web integrity, etc.