Drawing random numbers from a power law distribution in R

I am using the R package "poweRlaw" to estimate and subsequently draw from discrete power law distributions, however the distribution drawn from the fit does not seem to match the data. To illustrate, consider this example from a guide for this package: https://cran.r-project.org/web/packages/poweRlaw/vignettes/b_powerlaw_examples.pdf. Here we first download an example dataset from the package and then fit a discrete power law.

library("poweRlaw")
data("moby", package = "poweRlaw")

m_pl = displ$new(moby)
est = estimate_xmin(m_pl)
m_pl$setXmin(est)

The fit looks like a good one, as we can't discard the hypothesis that this data is drawn from a power distribution (p-value > 0.05):

bs = bootstrap_p(m_pl, threads = 8)
bs$p

However, when we draw from this distribution using the built in function dist_rand(), the resulting distribution is shifted to the right of the original distribution:

set.seed(1)
randNum = dist_rand(m_pl, n = length(moby))

plot(density(moby), xlim = c(0, 1000), ylim = c(0, 1), xlab = "", ylab = "", main = "")
par(new=TRUE)
plot(density(randNum), xlim = c(0, 1000), ylim = c(0, 1), col = "red", xlab = "x", ylab = "Density", main = "")

Resulting Plot, Red = Distribution Drawn from Fit

I am probably misunderstanding what it means to draw from a power distribution, but does this happen because we only fit the tail of the experimental distribution (so we draw after the parameter Xmin)? If something like this is happening, is there any way I can compensate for this fact so that the fitted distribution resembles the experimental distribution?