Bone marrow transplants can change a person's blood type because blood cell progenitor cells are transplanted into the recipient. That's pretty much the whole point: to remove cancerous progenitor cells (e.g. via whole body irradiation) or to augment insufficiently active bone marrow (e.g. aplastic anemia) with progenitor cells able to produce blood cells.
But the progenitor cells in bone marrow have basically only one fate: to become blood cells of some type, either red cells or any of a variety of white blood cells (leucocytes).
The bone marrow progenitor cells cannot become less differentiated such that they can become pluripotent stem cells, that is, they can't find their way into the testes and become sperm.
Forensic analysis of sperm is limited to visual analysis (presence, number, morphology, etc.), seminal fluid analysis (mostly enzymes or other substances found in everyone's semen), and DNA.
Although the ABO blood group antigens are primarily recognized as RBC antigens, they are expressed in a wide variety of human tissues and are present on most epithelial and endothelial cells. Seminal fluid of secretors contains alpha 2-seminoglycoprotein, consistent with blood ABO types.
In individuals who are "secretors", a soluble form of the ABO blood group antigens is found in saliva and in all bodily fluids except for the cerebrospinal fluid.
Blood type is only one potential component of semen. The secretions themselves come from the person's epithelial cells, not blood cells, so the secretions will not change with bone marrow transplantation, as blood cell progenitors do not become epithelial cells.
The most critical for identification purposes - DNA - comes from the sperm itself, and certain gene expressions (and enough of them) are tested for to make a positive identification possible. The DNA in sperm will only come from spermatogonial stem cells present in the early embryos onward.
So, no, there's no way a bone marrow transplant can change a non-blood related cells DNA composition.
Edit to address OP's edit:
The case explained by Dr. Alizadeh is in keeping with exactly what I explained above. She explained that blood type and blood DNA, which comes from white blood cells, which still have nuclei, changes in the recipient. But only the blood, not the semen, or DNA from a cheek swab (epithelial tissue). From the article:
...(a bone marrow transplant patient) his or her blood [a bone marrow recipient's] comes from the donor's stem cells. And so has the donor's DNA.
N.B. She only states that the recipient's blood will have the donor's DNA.
In her example, semen DNA matched a blood sample DNA in the DNA data base from a jailed criminal. It also matched the DNA profile of another person, the jailed person's brother, who was the marrow donor.
The conclusion, though it's not stated in an obvious manner, is that the perpetrator of the crime was the marrow donor, the jailed recipient's brother.
At first all the detectives were confused by this case. With good detective work they found out that both people had the same last names and were brothers.
They discovered that the person who was in jail received bone marrow from his brother several years earlier. So, his [the recipient's] blood DNA profile was the same as his brother's blood DNA profile. But his [the recipient's] cheek swab DNA profile was different from his brother's.
So, your new, (post edit) question:
Is it true that there have been situations where DNA mix-ups due to bone marrow transplants has lead to confusion during a criminal investigation?
This seems to be answered by the article you cite.
The actual case is discussed further here (Bone marrow donors risk DNA identity mix-up), repeated by the BBC here (Fears over transplant DNA mix-ups), and explained in more scientific detail here (The Interrogation of Mr. DNA, Part 3 of 3: Detection).
My original answer remains the same. Bone marrow transplants do not change the DNA of the recipient's other tissues. Just the blood.
This is my first answer on Skeptics, so comments on how to improve it are welcome.
Safety and impact of donor-type red blood cell transfusion before allogeneic peripheral blood progenitor cell transplantation with major ABO mismatch.
Blood Groups and Red Cell Antigens
Forensic Biology: Serology and DNA, Springer (PDF)