score:7
One of the sources quoted by the Wikipedia article is the United Nations Report of the Special Committee on the Problem of Hungary. If the document is genuine*, I would be inclined to give it much more credence than an unsourced sentence in an introductory paragraph to a Wikipedia article. On page 150, the report states that, on the evening of 23 October:
"... ΓVH men rushed from the entrance and began shooting in all directions. At least three people were killed - some say eight - and many wounded. For about twenty minutes the shooting continued from the windows of the building, resulting in more casualties among the demonstrators."
The report makes no mention of the body of a protester being wrapped in a flag and carried above the crowd. It does, however, state that
"The bloody clothes of the first dead were carried through the city and people rallied behind them in procession."
None of those killed in the early stages of the revolution are named. However, from the details presented in this report, it seems that any impression that "if one student hadn't died, the revolution never would have started" is probably mistaken.
* Although there seems to be no doubt that a document by that name exists, I was unable to locate a copy of the report on the United Nations Official Document System search site (This may be because of the age of the report, or that it, together with associated documents, were classified Strictly Confidential when published, as shown in the Registry Section Summary (p711)). As a result, I cannot confirm that the report linked above is the actual report issued by the UN Committee. With that caveat, however, there does not seem to be anything in the content of the report to suggest that it is not genuine.