Reasoning from single incidences is not evidence in favour of 'white privilege' or any form of discrimination in any situation where there is natural variance in outcomes. I'm sure you can find many instances of individual black offenders being given lighter sentences than individual white offenders. If someone used one such example to 'prove' racial bias didn't exist I'm pretty sure you wouldn't accept it as persuasive.
This is the problem with concepts like 'white privilege' or 'systemic racism': they cause people to consider every case as being racially driven and thus vastly overstate the degree of discrimination
even if such discrimination exists on average. They are also ubiquitous, so any differences in outcomes automatically get put down to privilege/racism without the need to actually prove anything.
Individual cases are memorable, easy to share, discuss and promote, but ultimately they are generally not evidence for what is claimed as there are too many unknowns.
Without clear and decisive evidence of racial favouritism or discrimination you can't tell in any individual case
even if such discrimination exists on average.
Black offender gets a harsher than average sentence = racism. White offender gets harsher than average sentence = not racism. White person calls the cops on black people minding their own business = obviously racist. White person calls cops on white people minding their own business = interfering busybody.
From the article you linked to:
One important result from Table 6 is that females receive even shorter sentences
relative to men than whites relative to blacks. The discrimination literature gen-
erally argues that females are objects of discrimination and receive worse out-
comes. In sentencing, however, women receive better outcomes, consistent with
women’s being treated paternalistically in court. Although some contend that the
sentencing guidelines harm women, studies have usually concluded that females
are sentenced more leniently than males.
Why then assume 'white privilege' over 'female privilege', and If black women receive lighter sentences than white men, how does this fit into the narrative?
Also, while I agree that there are certainly good reasons to believe black people, on average, are more harshly treated, there are too many variables to be certain that such discrimination exists, or to what extent it exists.
Limitations of studies are discussed in this paper in both the literature review and the conclusion despite it not arguing against the idea that discrimination exists:
https://www.povertyactionlab.org/sites/default/files/publications/210 Do Judges Vary Sept 2010.pdf
The main idea being that there might be unobservable variables having significant effects and that differences seem to vary by crime type
For example (from your paper):
The racial and gender disparities are largest for bank robbery and
drug trafficking. Most of the difference between Hispanics and whites is from
two crimes—drug trafficking and firearm possession and trafficking. The edu-
cational differences are generated primarily by drug trafficking and are not
statistically significant for other offenses.
It's not as self-evident as is often made out.