To be fair to the Germans the mud hut would probably apply to almost all the countryside in the empire. The prosperity of Rome wasn’t spread out that evenly, both geographically and socially.
There are two things to clarify in this:
The Germanic tribes in the 1st-3rd centuries BCE-AD were monumentally impoverished and technologically backward, including compared to their non-Roman neighbors in Gaul before it was conquered.
While the prosperity of Rome was concentrated in urban areas and the upper class, there is considerable evidence of increased living standards, including in the construction of rural houses, during the height of the Republic and Principate.
There are two things to clarify in this:
The Germanic tribes in the 1st-3rd centuries BCE-AD were monumentally impoverished and technologically backward, including compared to their non-Roman neighbors in Gaul before it was conquered.
While the prosperity of Rome was concentrated in urban areas and the upper class, there is considerable evidence of increased living standards, including in the construction of rural houses, during the height of the Republic and Principate.