Earlier quoted context omitted.
Injuries did increase, though, and I can't think of a plausible mechanism that would somehow cap expected outcomes at "injury but not death".
So we were talking about excess deaths, which means that supporting your argument with a paper that argues that a previous finding of excessive deaths was flawed is probably not the strongest argument you could make. Increased number of injuries but not deaths could be, for example, (purely making things up off the top of my head here) due to higher levels of distractedness among average drivers due to fear of terror…
That's not a remotely plausible model though. There are recorded cases of e.g. 1.6 seconds of distractedness at high speed causing a fatal collision. Anything that increases road injuries is almost certainly also increasing deaths in something close to proportion, but a given study size obviously has a lot more power to detect injuries than deaths.