I haven't read anything definitive and just gone on what I have heard people (who should know about this ) have said. is the wording you have given the official definition?
Actually, I've now looked it up
https://assets.publishing.service.g...l-certificates-of-cause-of-death-covid-19.pdf
example of death certificate entries below (with three sequential parts fo fill in):
(a) Disease or condition leading directly to death. Interstitial pneumonitis
(b) other disease or condition, if any, leading to I(a) COVID-19
c) other disease or condition, if any, leading to I(b) primary adenocarcinoma of ascending colon
As far as I can make out from the document, from a public health point of view, the most important line is line c, as this is the condition considered to have initiated the fatal sequence of events to death, suggesting that without condition c, condition b would not/may not have caused death. So depending on the question, it would seem that deaths where the final line is Covid-19, are clearly caused by Covid -19, but deaths with a line below the Covid-19 entry are deaths with a more complex cause of death.
EDIT: this way of completing death certificates seems to be a WHO standard, so I wonder what the experts at the daily briefings are referring to when they say that in some of the European countries they aren't always including Covid-19 on the death certificate unless it's considered the cause of death.