I don't know. They could be MZ.
It's not that unusual for parents of MZ twins to feel the need to have genetic testing "to know for sure." I think if they have been hearing from birth onward that "they look so different" or "they aren't identical, are they?" or "they can't be identical -- they look so different!", then that could lead to them being hung up on the issue. I have doubts about my boys sometimes (although the moms here have said I am in denial, that they are DEFINITELY mz
) but I know that I do get defensive about it (internally) if someone questions it in a certain way. For instance, I remarked with surprise that they weren't getting their teeth right after each other (they have had the same pattern but it's a week or more apart), and their doctor shot me a look and said, "What, you don't think they're identical, do you?" I felt so defensive, and said something like "Well, I know they don't look 'identical' but they are supposed to be monozygotic since they shared a placenta, so they are identical in that sense."
And I felt that way when she (same doc) scrutinized them on our first newborn visit and said she didn't think they were identical. I shrugged and said "They're supposed to be, but we didn't have the placenta examined so I don't know absolutely for sure, but the early ultrasound was fairly conclusive that it wasn't fused." Then at their 6 week or 2 month visit or something, she was looking at them and said, "These twins are not identical. I really can tell them apart and would not expect to do so this easily."
I didn't mention that I've heard how sometimes the babies are most different from each other at birth and then grow to look more and more alike, harder to tell apart.
(To be fair, she was looking back and forth between them when she saw them at 7 months, and she said, "Maybe they are identical after all. They are hard to tell apart."
My doctor is a fine person and isn't/wasn't being mean or obnoxious. She was just talking, each time. It's probably just my own uncertainty (I've become more certain lately, for some reason) that made my feelings in response amplified and uncomfortable/defensive.
But constant questioning (from the world at large, not specifically from family), in the face of whatever "authoritative" or certain medical feedback they received during the pregnancy, could put a chip on their shoulders about the zygosity. And that could result in them bringing it up, feeling/seeming defensive, managing to say something about the genetic testing results even if nobody asked, etc.
Do you think they are just lying about the genetic testing? (Did they put it in the baby book or something? You could ask if they saved the results, I guess.) You mentioned the possibility of the lab not being reputable....of course it's possible but that seems kind of a long shot to me. I guess you could ask what lab they used and how they found it/chose it. Chances are, if they found out about testing online (as I did), then they heard about it through some twin forum and got feedback about where to go and what the options are. (This seems to be a topic on every twin forum I've visited.) I hear some labs frequently mentioned, and they are the ones that people (here, for instance) have vouched for as reputable.
I think if I wanted to engage the topic, I'd just ask how they knew that the twins were identical during the pregnancy. Maybe not that question directly, but questions that would draw out relevant information. Like asking how far along she was when they found out she was carrying twins. (How early was the first ultrasound?) I had our first u/s at 14 weeks and it was early enough to be nearly certain about the placenta, but two weeks earlier and they could have literally counted the layers of the membrane between them. (Four layers would have meant di/di and a fused placenta, but two layers would just be the individual amnions touching, without the additional chorionic membranes for each baby, which would confirm the single placenta.) As it was, they knew the membrane was very thin (points to being two layers rather than one) and it came to a clean "T" where it met the placenta/chorion....there wasn't a "buildup" of membrane layers at that juncture.
So.....you could ask if there was any risk of TTTS or if the babies were safe because they had their own placentas. And if you learn that they had two placentas, then there is no way a doctor could have confirmed identical during pregnancy. If there was a single placenta, and if you learned that she had a fairly early ultrasound, then there's a good chance that a doctor telling them that the twins were identical because they shared a placenta was an accurate assessment.
If, instead, they are hung up on the girls being identical for the reasons suggested (think that id. twins are "cooler," think that fraternal twins aren't "real" twins, or are sensitive about the suggestion/assumption that they used assisted reproductive technology of some kind if the girls are fraternal), perhaps the term they are looking for is "spontaneous." They were spontaneous twins.
Unless you think they would outright lie about lab results, I'd be inclined to think that they are identical twins and they just don't look much alike, and it bugs the parents that everyone seems to question it, or that people just assume that they aren't MZ. As to why twin type matters......I don't know why it should. There are good reasons to know one way or another, but a lot of it just has to do with curiosity, and probably other feelings.