in the way that one single paper can prove opposing things simultaneously, depending on how it is sliced
general rule of thumb is to go with what the authors write in the abstract (and get a second opinion for confirmation) and to be very wary when someone tries to read between the lines, that's usually misleading.
As a lay person, the part which would jump out at me there (and perhaps similarly for a dedicated conspiracy theorist) is the "Note: Deaths may or may not have been due to COVID-19" caveat we seem to often get with these studies and figures.
Again, as perhaps quite a simple-minded person, I don't particularly understand how it could possibly be valid for government representatives, medical representatives, the media, or anybody else to assess the differences in deaths (from covid) between the vaccinated and unvaccinated when the unvaccinated is inclusive of cases that may have nothing to do with covid at all.
What you do in a case like this is click through to the original source (it's easy here, but sometimes it involves several steps or a search engine - or you could ask on Metabunk), and find more background information:
Importantly, not all hospitalizations and deaths of those fully vaccinated and diagnosed with COVID-19 are due to COVID-19 or have a known cause at the time of reporting. The CDC reports that as of July 19, of 5,601 hospitalized breakthrough cases, 27% were asymptomatic or not related to COVID-19 and of 1,141 fatal cases, 26% were asymptomatic or not related to COVID-19. States differ in whether they provide this detail. DC, for example, reports that as of July 11, 50% of hospitalized breakthrough cases were due to COVID-19, 19% were not, and 31% were of unknown reason. However, few states made these distinctions. Where they did, we only included breakthrough hospitalizations and deaths due to COVID-19. In other cases, some of these breakthrough events may be due to causes other than COVID-19.
This is about vaccinated people; they later say the same thing about unvaccinated people.
So, now that I've looked this up, I know:
* the authors did their best to get good data
* but the databases don't always provide the data
* where they do, they use it, so you can dig into the tables and look only at the states that make this distinction, if you like
* but they don't look that different than other states
So I have already learned that there's nothing anyone is hiding
I have also learned that this applies to vaccinated and unvaccinated hospital patients alike, so I know that I mentally need to rewrite your complaint: "how it could possibly be valid [...] to assess the differences in deaths (from covid) between the vaccinated and unvaccinated when both the unvaccinated and the vaccinated is inclusive of cases that may have nothing to do with covid at all
". Your complaint had an aspect of 'the unvaccinated are treated unfairly' that simply vanished,
now that we know that.
Let's say someone (vaccinated or not) has a car accident, they get hospitalised, and the hospital runs a routine Covid test on them, which comes back positive; and because they're now hospitalized with Covid, but not because of Covid, they're an error in this statistic in some states. The question is, does this affect the conclusions of the statistic in any way, and if so, in what direction and by how much? That's something you're not going to be able to decide as a layperson; you'll just have to trust the authors, the publishers, and their experts. If you're unsure, look for other studies, and see if they confirm or contradict the finding.
My personal opinion is that it didn't matter much; and that it matters even less now because that number went down as the vaccination rate went up, so that number is very different today anyhow.
(If you have questions about a study, but find it too hard to read, I'm usually happy to answer questions as best I can.)