The incident highlights the tension between the right of an executive to privacy regarding sensitive health matters, and investors' wishes for transparency when an important corporate figure is sick or incapacitated. Regulatory disclosure rules can leave much at a public company's discretion.
Mr McDermott slipped on the stairs at his brother's US home during the night while holding a glass of water. He fell on the glass and briefly lost consciousness.
He could have bled to death, according to Mr Plattner, but regained consciousness and his cries for help were heard in time. Initially doctors succeeded in saving his eye, but following an infection it was later removed. He now has an artificial left eye.
"I'm still alive, and that isn't a foregone conclusion after such an accident. Therefore, strange though it sounds, I am happy . . . I feel stronger than before, more passionate, more alive. I am completely available for SAP and committed to my job," Mr McDermott told Sueddeutsche Zeitung, a German newspaper, adding that he would be able to fly again in October.
Like many companies, SAP has a back-up plan in the event of an accident involving a senior manager, but Mr Plattner told Wirtschaftswoche, a German magazine, this was not needed because Mr McDermott was on the mend.
SAP told employees in an internal email in July that Mr McDermott had an accident, and the company confirmed to Bloomberg that month that the chief executive had been discharged from hospital, was in a good condition and was expected to make a full recovery, without providing details of the injury.
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Mr McDermott was well enough to dial into SAP's second-quarter results call with investors later in July.
Mr Plattner noted the accident had happened during the quiet summer months and had therefore not affected SAP's business.
Mr McDermott said he had the confidence of the whole supervisory board and expects to attend an SAP board meeting in October.
The issue of CEO health was debated earlier this week when Harald Krueger, BMW's chief executive collapsed on stage during a press conference at the Frankfurt motor show. The carmaker said he suffered a "moment of dizziness" but was "recovering well" at home.
Due in part to privacy concerns and the difficulty of deciding whether an executive's illness or injury is sufficiently serious to warrant being made public, regulatory disclosure rules typically have few specific clauses on health matters.
BaFin, Germany's financial regulator, said a listed company must release information likely to have a significant impact on its share price. While this in theory includes health issues, any share price movement would depend on the indispensability of the executive and the nature of the illness.
SAP said on Thursday that it "evaluated the situation and came to the conclusion that there was no obligation for an ad hoc [announcement]" - a reference to how company news that would affect its share price should be released in an ad hoc statement.
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In 2004, Steve Jobs, then Apple's chief executive, revealed he was undergoing treatment for pancreatic cancer but thereafter the company was guarded about the details of his condition.
That was a source of frustration for some investors because his wellbeing was considered so paramount to Apple's prospects and his increasingly gaunt appearance suggested he was unwell.
In contrast, Warren Buffett, the billionaire investor, was quick to disclose full details of his diagnosis and treatment for prostate cancer in 2012.
The Securities and Exchange Commission, the US financial regulator, does not place a specific requirement on a public company to disclose an executive's illness in a so-called 8-K report to investors.
However, the SEC wants companies to consider health issues for "materiality" - so if the illness is serious, it could require disclosure.
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The Financial Conduct Authority, the UK regulator responsible for the listing regime, requires public companies to make judgments about whether illness changes a director's role, among other things.
If the director cannot perform his job because of long term sickness, the company would need to disclose that information as soon as possible.
In 2011, Lloyds Banking Group announced that António Horta-Osório would take a leave of absence from his role as chief executive, due to stress and fatigue.