This is probably true, but we don't actually know yet. The trials weren't big enough to give quantitative results on severe disease or death.
From the Pfizer and Oxford/AZ phase 3 trials the results were (two doses)
Pfizer active: one severe disease
Pfizer placebo: nine severe disease
AZ active: zero severe disease
AZ placebo: ten severe disease
What does this tell us? severe disease is much less likely, but not impossible on active vaccine full dosing regime. But the numbers are small, so it would be unwise to try and quantify. Confidence limits on % protection against severe disease are not included in the trial results, probably for that reason. I'd guess a confidence interval could be as wide as 70-100% from such a result - and it of course depends on the population. In the real world our initial population vaccinated is massively skewed towards older people, and they may have a different level of protection to the average person on the trial.
There is no clear data reported on the single dose (because everyone on the trial got two), but the data on the interval between the doses shows similar results, albeit with even lower numbers. Other data on immune response suggests that we should expect similar short term efficacy on the single dose, but there is no hard data on this. That's presumably why Pfizer have declined to support the delayed second dose strategy.
There is no data reported on deaths. We should expect a reduction in mortality along with the reduction on severe disease, but this isn't absolutely certain that it's proportional - it could be (much) better or worse. In cancer, for instance, drugs often delay progression of disease but ultimately don't make any difference to ultimate time to death. It *might* be that if you are particularly susceptible to COVID you die regardless of vaccination.
None of this is intended to suggest the vaccines are ineffective, just that we should be a little cautious about *how* effective until we learn more. We should start to know over the next couple of months what the real world protection is.
Pfizer:
https://www.nejm.org/doi/full/10.1056/NEJMoa2034577 (table S5)
Oxford AZ:
https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)32661-1/fulltext (table 5)