You are not completely right

In Acrobat CMYK Black is OK it is only 100% K
RGB black by my opinion is OK exported - its CMYK conversion depend only by color profile used by you (The same is and in the photoshop)
A litlle strange is thing with text overprint... in Acrobat its not showed... maybe acrobat didnt understand that there is overprint, but same PDF opened in Illustrator shows that, yes, you have given overprint of black text!

More strange is that same PDF didnt want to be opened or imported in Corel X3, same thing is and after resave in Acrobat..... maybe has something that must be fine-tuned there