Dr. Ioannidis first expressed this sentiment early in the pandemic, writing on March 17^th, 2020 that “A positive test for coronavirus does not mean necessarily that this virus is always primarily responsible for a patient’s demise”. Though this belief has since become widespread, this is the earliest instance I found of someone asserting that the virus might not to blame when someone dies after contracting it. The idea that many people are dying with the virus, not from the virus, remained a feature of his interviews and publications. It’s worth quoting Dr. Ioannidis’s statements in full:

• Now, your point that we’re literally counting, as opposed to estimating, deaths from coronavirus is correct. But I’ll push back that this may not yield mortality figures as accurately as people think. Because of the attention on coronavirus, we’re better at knowing that a deceased person had coronavirus than had the flu. This means we’re good at knowing when someone died with coronavirus — but not necessarily that they died from the infection. We assume that dying with coronavirus is dying from coronavirus. (Medscape)
• So, this is also an open question. Because for the data that we have more mature and detailed information, like the data from Italy that has already through the peak of their epidemic wave, we realize that 99% of people who die with this virus have other reasons as well to die. On average, they have close to three other reasons to die. On average they are 80-years-old with other comorbidities, as we say, and there’s quite some debate on whether these people would have died anyhow, if not immediately, you know, perhaps in a few days or in a few weeks or a few months. In our country we see a fairly similar picture. We see that people who are disadvantaged, poor people, creating even further inequality in the population through COVID-19, seem to be very hard hit. We see that the age of death on average is a little bit lower compared to European countries, in the range of 73 or 74-years-old, and we see again lots of comorbidities in people who die with COVID-19. It’s very hard to say how many of these people would have died anyhow and how much is the direct contribution of the virus. These data are evolving, but if anything they suggest that the burden of disease as we call it, the number of person-years lost, how many years of life are being lost, is much less than even what the number of deaths would suggest. This is not to minimize the problem. It is a serious problem. (Fox; start listening at 5:05)
• COVID-19 has become a notifiable disease, so it is readily recorded in death certificates. What we do know, however, is that the vast majority of people who die with a COVID-19 label have at least one and typically many other comorbidities. This means that often they have other reasons that would lead them to death. The relative contribution of COVID-19 needs very careful audit and evaluation of medical records. (Greek Reporter)
• Finally, a major question that should be answered is the causal contribution of SARS-CoV-2 infection to related deaths. It is difficult to differentiate between deaths with SARS-CoV-2 infection and deaths caused by SARS-CoV-2 infection because the vast majority of patients who have died had 1 or more other major pathologies (98.8% with at least 1 comorbidity, and 48.6% having 3 or more diseases) that contributed to their death. (JAMA Internal Medicine)
• When I made that tentative quote (estimating that COVID-19 will cause fewer than 40,000 deaths in the US), I had not considered the impact of the new case definition of COVID-19 and of COVID-19 becoming a notifiable disease despite being aware of the Italian experience where almost all counted “COVID-19 deaths” also had other concomitant causes of death/comorbidities. “COVID-19 death” now includes not only “deaths by COVID-19” and “deaths with COVID-19”, but even deaths “without COVID-19 documented”. (Int J Forecast)
• The number of COVID-19 deaths can be both undercounted and overcounted, and the relative ratio of over- and under-counting varies across different locations. In most European countries and the USA it is more likely to be overcounted, especially if we are talking about “deaths by COVID-19″…For COVID-19 we are in early days, and we need to be careful to dissociate deaths from COVID-19 versus deaths that happened because of the disruption induced by lockdown. (Greek Reporter)
• Another observation that has emerged is that many of these people (in Italy) probably would have had very limited life expectancy in the absence of that infection, and it still remains to be decided how many of these infections are deaths with SARS-CoV-2 versus deaths by SARS-CoV-2, meaning that the virus has the key influence on the outcome rather than just giving a final kick or participating among many other factors in shaping the outcome, but these people having multiple other reasons that they would have a very poor endpoint and eventually die, many of them. (Daily Motion; start listening at 18:45)

Likely there are other instances where he expressed similar sentiments of which I am currently unaware.