The NYT in its article "A Coronavirus Mystery Explained: Moscow Has 1,700 Extra Deaths" and FT in the article Russia’s Covid death toll could be 70 per cent higher than official figure" from May 11, said that data released by Moscow’s city government on Friday shows that the number of overall registered deaths in the Russian capital in April exceeded the five-year average for the same period by more than 1,700. That total is far higher than the official Covid-19 death count of 642 - an indication of significant underreporting by the authorities.
Within two days, on May 13 (the day that the TASS' article was also published), the Moscow City Health Administration’s statement admitted that, indeed, over 60% of deaths from COVID-19 were accounted in Russian statistics as deaths “from obvious alternative causes” such as heart attacks, stroke, cancer and others. The same principle of attribution of deaths of patients with coronavirus is implemented in at least several Russian regions, for example, in the Chelyabinsk region: here, official death statistics openly divides those with confirmed coronavirus into those for whom COVID-19 became the "main" cause of death with those who are classed as having had "concomitant disease". For comparison, see the principles of WHO. Indeed, coronavirus may trigger other diseases, such as heart attacks, but without coronavirus the victim may have had been alive.
Russian MFA's threatened to cancel the accreditation of both NYT and FT in Russia. On May 18, the NYT published a letter of response by the Head of Moscow's health department as an "opinion": "We perform an autopsy in every case, and therefore we are confident in the accuracy of our data. An increase in mortality rates is natural with an increase of acute respiratory viral infections, which aggravate the underlying illnesses".
The practice of a right to response has nothing to do with "being caught juggling facts".
See more disinformation cases on the coronavirus.