#1 seems possible with Covid given the preliminary data reported from one of the Covid vaccine trials, which reported lower efficacy on asymptomatic transmission. It's also been observed with flu vaccines, although the picture there is a lot more complicated by a longer history of, multiple vaccinations/infections, faster strain evolution (compared to coronavirues etc.
#2 seem possible based an animal (monkey) model of Covid, which found that vaccine candidates reduced replication rates differently in lower vs upper respiratory tract.
Also note that #1 and #2 are not independent hypotheses, as #2 can cause #1, although other factors can contribute to #1 as well.
#3 seems very unlikely to me given the substantial antibody seroconversion observed with Covid vaccines. Also I'm not aware of an approved vaccine (for anything) that doesn't substantially cause seroconversion, but in the oddball bin, I did find a study on a Japanese encephalitis vaccine candidate that seems to fit that description, again in an animal model. It seems that vaccine somehow affected only/mainly the primary cytotoxic T-lymphocyte (CTL) activity but not the neutralizing antibodies.
The article you linked explains what they mean by that
Because the shots from Pfizer and its German partner BioNTech SE avert symptomatic cases of Covid-19, their wide use could prevent virus transmission, the FDA staff report said. But if the vaccine doesn’t work as well in infections that lack symptoms, those cases “in combination with reduced mask-wearing and social distancing could result in significant continued transmission,” according to the staff report. [...]
Pfizer expects to report data on whether or not its vaccine stops virus transmission in the first quarter of 2021, Chief Executive Officer Albert Bourla said on Tuesday at a press briefing held by the International Federation of Pharmaceutical Manufacturers & Associations.
TLDR: data insofar tells us something about vaccinated people who didn't get symptomatic Covid. This was remarked earlier when the data was released:
The primary efficacy being reported is based on symptomatic cases. So this does not tell us whether it prevents the same level of infections nor anything about onward transmission.
it seems strange that the vaccine would prevent the disease but not prevent transmission
that's actually the case (to some extent) with flu vaccine(s) in that they lower symptoms in infected people too, perhaps to the point where someone would not report symptoms (e.g. they might get myalgias but not fever)
A total of 155 cases of influenza (A/H1N1, n=69; A/H3N2, n=66; A/untyped, n=3; B, n=17) were identified, of whom 111 (72%; A/H1N1, n=44; A/H3N2, n=52; A/untyped, n=3; B, n=12) [...] In multivariate analysis, vaccinated individuals were significantly less likely to report a fever >101° F (OR 0.24; 95%CI [0.10, 0.62]) and more likely to report myalgias (OR 3.31; 95% CI [1.22, 8.97]) than vaccinated individuals. Among patients with A/H3N2 infection, upper respiratory and total symptom severity scores were significantly lower for vaccinated patients during the first two days of illness, and differences in total symptom severity persisted over seven days (p<0.05 for all comparisons). Differences across additional symptom categories (lower respiratory and systemic) were also observed throughout seven days of illness in bivariate analyses. Differences in symptom severity were not observed between vaccinated and unvaccinated participants with A/H1N1 infection.
And discussing similar papers:
Influenza vaccine-associated disease attenuation has also been observed in several pediatric studies, though there has been considerable variability in study design and the definition of severity. Jain and colleagues reported decreased “moderate-to-severe” disease in vaccinated children, where severity was described as a combination of body temperature >39° C, otitis media, lower respiratory disease or serious extra-pulmonary manifestations [ref].
More recently, post-hoc analyses of live attenuated influenza vaccine (LAIV) efficacy trials demonstrated that in >1,600 children aged 2-17 years, relative efficacy was higher in the prevention of severe as opposed to mild disease. Variability of these effects by season and influenza types and subtypes was also observed [ref]
One can hope that vaccines against SARS-CoV-2 (which being a coronavirus mutates slower--at about half the speed of influenza[s]) will fare better. (There are some additional factors to discuss here, but maybe someone else wants to delve into that.)
Regarding why that happens with flu, generally speaking:
Even though strain-specific neutralizing antibodies confer protection against infection with matching influenza virus strains, non-neutralizing antibodies and cellular immune responses to the virus that are cross-reactive to other viral strains also contribute to reduce disease severity and infectivity.
Regarding Covid, there's actually a recently published preliminary result on one of the vaccines and asymptomatic infection:
vaccine efficacy against asymptomatic transmission was 59% in the group that received a half dose followed by a standard dose (seven cases among 1120 participants versus 17 cases among 1127 participants in the control group), but just 4% in the group that received two standard doses (22 among 2168 participants versus 23 among 2223 for the control). The researchers said, however, that as this was a secondary outcome, additional confirmation was still required.
Nobody seems to know why just yet.
But at least one animal model for Covid-19 suggests that vaccines may be better a reducing replication in the lower than in the upper respiratory tract:
Recent studies have reported the immunogenicity and protective efficacy of several candidates for a COVID-19 vaccine in the rhesus macaque model. [...] the vaccines tested so far have induced binding and neutralizing antibodies and have resulted in substantial reductions of viral replication in the lower respiratory tract, and—to a lesser extent—the upper respiratory tract, following challenge with SARS-CoV-2. These findings raise the possibility that vaccines may be more effective at blocking disease of the lower respiratory tract than of the upper respiratory tract.
(One has to keep in mind that such animal model don't always match what happens in humans.)