In a controlled setting, sunblock will always affect vitamin D production, whether you expose for 20 minutes or 60 minutes or 120 minutes, or whether you test 37 subjects or 370 subjects.
The reason is that 7-dehydrocholesterol is photolyzed by UV light in the 280-320nm range (mostly UVB) to previtamin D. Sunblock works to absorb UVB (and usually UVA) to prevent it from penetrating your skin. Thus sunblock limits the amount of UVB penetrating your skin, and limits your ability to make vitamin D.
That being said, yes, you will still make some vitamin D with sunblock on because sunblock is not perfect at absorbing UVB. Just not as much as you would without.
The reason melanoma incidence is increasing is because of a "diagnostic drift," similar to what we see in the rise of psychological disorders: http://www.ncbi.nlm.nih.gov/pubmed/19519827
We are more routinely getting skin lesion check ups and dermatologists and oncologists are more and more cautious, leading to an ever-increasing incidence of stage I melanoma. However, we're not really seeing an increase in later stage melanoma, meaning that the "true" incidence of melanoma is not increasing.
It's sort of a huge public health scam. The dermatologists are using this vanity metric of increased diagnoses as evidence that we're in the middle of a melanoma/skin-cancer epidemic, when it's simply not the case. Not that safe sun exposure practices shouldn't be promoted, but the motor behind these messages is a bit of a scam.
Sunbathers who use sunscreen tend to not have lower vitamin D levels than non-sunbathers who don't use sunscreen, because, well, people who don't use sunscreen don't get sun exposure anyhow.
Also, when the human genome was evolving, sun exposure accounted for 90%+ of all vitamin D intake, diet accounted for less than 10%. We know this by looking at the diets and vitamin D levels of hunter gatherers.
The researcher's comment IS false based on the information we have available to date. We do not know if fish oil is worthless or not. The researcher implicitly states that he knows fish oil is worthless based on the evidence to date, when the evidence to date is much more mixed.
The NEJM article in this thread is much better evidence -- a 13k RCT that found no statistically significant benefit in 1g/day of omega 3s. On the other hand, there was a large 11k trial in the 90s that did find benefit 1g/day of omega 3s:
http://www.ncbi.nlm.nih.gov/pubmed/10465168
The VITAL study underway will be interesting. It's the largest trial to date on fish oil and is looking at a healthy normal population, as opposed to those with CVD or high-risk of CVD.
There is a 20,000 person 2x2 randomized controlled trial underway right now looking at how useful fish oil is in preventing disease: http://www.vitalstudy.org Results will be out around 2017-2020.
An observational study from the 1970s and a critique of an observational study from the 1970s will carry little merit compared to a 20k RCT.
Knowing that we'll have better data in 5 years, the comment by the researcher is nauseating: "They simply don't do anything for you. The people should know that it doesn't help to prevent heart disease." Since we haven't quite reached an apex in research in fish oil, the comment is short-sighted and is overstating what we know about fish oil to date.
The reason is that 7-dehydrocholesterol is photolyzed by UV light in the 280-320nm range (mostly UVB) to previtamin D. Sunblock works to absorb UVB (and usually UVA) to prevent it from penetrating your skin. Thus sunblock limits the amount of UVB penetrating your skin, and limits your ability to make vitamin D.
That being said, yes, you will still make some vitamin D with sunblock on because sunblock is not perfect at absorbing UVB. Just not as much as you would without.