bacteria and mitosis

[IntelInside]

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I was under the impression from EK BIO lecture 3 where it explicity states:

Bacteria (prokaryotes) CAN'T undergo meiosis or mitosis, and they can ONLY undergo Asexual Reproduction. The type of cell division they are capable of undergoing is called binary fission, which exhibits exponential growth.

But here in one question it asks "when examining the blood of a patient with a disseminated bacterial infection, the researcher expects to notice mitotic division being performed by which of the following cells?"

I. red blood cells
II. white blood cells
III. infectious bacteria

and the right answer is III only. WTF???? this is contradictory to what the book says. They dont undergo mitosis they perform binary fission and since all blood cells cant undergo mitosis/reproduction this question should have a "none of the above" answer. Is this correct?

 

[zkbd9]

The only thing I could think of is the case of a retrovirus. Basically, it is an RNA virus that uses reverse transcriptase to synthesize DNA. This retroviral DNA becomes incorporated into the host DNA. I'm assuming that if retroviral DNA is in the host cell's DNA then it can undergo mitosis. HIV works like this.