If you construe "violence" broadly enough, then yes, this is true.
But a broad interpretation misses most of the nuance that matters in practice.
If you conceive of state violence instead as something like "the probability that you will get tortured, or beaten, or lose your money or property for things like speaking out against those in power", then the original statement is no longer true, and there are stark differences between living in modern western democracies and actually violent regimes -- which of course there are.
The “monopoly on violence” just means that the government is the only one that can legitimately use force to enforce its rules.
No polity has an actual monopoly on violence within its borders because anyone can make a shiv and stab someone or start their own violent gang or militia.
But a broad interpretation misses most of the nuance that matters in practice.
If you conceive of state violence instead as something like "the probability that you will get tortured, or beaten, or lose your money or property for things like speaking out against those in power", then the original statement is no longer true, and there are stark differences between living in modern western democracies and actually violent regimes -- which of course there are.