How to access attribute values in raster using R's stars package?

Question

I have downloaded a publicly available file containing a set of datasets in .tif format. Using R's stars package, I would like to take at look at the attribute values present in the raster, but I am facing some difficulties when trying to do so. I managed to perform this task using a toy file that comes with the stars package, but the same steps did not work with the data that I am using.

Below I provide the details of what I managed to do and what I did not. First I show how everything went fine with the toy data present in the stars package.

# Libraries
library(stars)

# Example with toy data
dfrt <- read_stars(system.file('tif/L7_ETMs.tif', package = 'stars'))
dfrt[[1]][1:5, 1:5, 1]                              # Displaying (a subset of) attribute values
# dfrt[1, 1:5, 1:5, 1][[1]]                         # Produces the same result as above
# dfrt %>% slice(., along = 'band', index = 1) %>% 
#    .[[1]] %>% .[1:5, 1:5]                         # Produces the same result as above

The above code produces the following intended result:

, , 1

     [,1] [,2] [,3] [,4] [,5]
[1,]   69   74   68   61   60
[2,]   69   68   64   61   63
[3,]   63   59   61   63   65
[4,]   60   58   60   60   58
[5,]   61   58   59   56   57

I tried to do something analogous with a dataset that is publicly available, but I did not succeed. The code for downloading and reading the file was the following:

# Obtaining the file
download.file(paste('https://dataverse.harvard.edu/file.xhtml?persistentId', 
                    'doi:10.7910/DVN/YSWMDR/FUQ16M&version=1.1', sep = '='), 
              'BUPR.tar.gz')
untar('BUPR.tar.gz', files = file.path('BUPR', 'BUPR_2010.tif'))

# Reading the file
dfdp <- read_stars('BUPR_2010.tif', proxy = TRUE)

The characteristics of the data that I downloaded are the following:

stars_proxy object with 1 attribute in 1 file(s):
$BUPR_2010.tif
[1] "[...]/BUPR_2010.tif"

dimension(s):
  from    to   offset delta                       refsys point values x/y
x    1 18459 -2356399   250 USA_Contiguous_Albers_Equ... FALSE   NULL [x]
y    1 11615  3172999  -250 USA_Contiguous_Albers_Equ... FALSE   NULL [y]

Writing something similar to what worked with the toy data does not produce the intended results. This problem seems embarrassingly trivial, but I think that my lack familiarity with this kind of data is preventing me from finding the solution. How do I perform a task similar to what I did with the dfrt data?