This connection has been reported by several groups, in credible journals (I left a few references below). The study and news article you are referring to is confirming earlier findings, it is not the first to report this. In the examples I've seen, the studies rely on large datasets, for example, incidences in an entire country, in order to show a significant effect. Despite being significant, the effects are modest; that is, we are talking about fractional increases that would account for a tiny minority of acute MI over an entire year period, but is significantly greater given a current week.
Because of the marginal significance of the effects, they could be overstated due to biases in publishing significant results, but I don't see much reason to be specifically skeptical of these findings versus others. The fact that it is true for both MI and stroke in one dataset is further support it is a real effect, but since the effect is only seen on certain days of the week and those days differ between studies it could still be spurious or smaller than reported. These studies also tend to show the opposite effect on daylight savings time transitions in the other direction, so they don't necessarily support elimination of daylight savings time.
I find the best resource for finding individual studies reported in the news media is Google Scholar, scholar.google.com - if you search for the author's name, a few key words, and a year if you have it, you can likely find the original work. Some studies may be more difficult to access in full text if you don't have access to a university library, however.
Janszky, I., & Ljung, R. (2008). Shifts to and from daylight saving time and incidence of myocardial infarction. New England Journal of Medicine, 359(18), 1966-1968.
Sandhu, A., Seth, M., & Gurm, H. S. (2014). Daylight savings time and myocardial infarction. Open heart, 1(1), e000019.
Sipilä, J. O., Rautava, P., & Kytö, V. (2016). Association of daylight saving time transitions with incidence and in-hospital mortality of myocardial infarction in Finland. Annals of medicine, 48(1-2), 10-16.
Sipilä, J. O., Ruuskanen, J. O., Rautava, P., & Kytö, V. (2016). Changes in ischemic stroke occurrence following daylight saving time transitions. Sleep medicine, 27, 20-24.
