No, it really isn’t. It may lead to insolvency, but that is by no means a foregone conclusion and can play out in different ways.
At a simple scale, If I own a $200k home outright and have $50k in credit card debt that I cant pay then I file for bankruptcy, negotiate with creditors to sell my home and pay the debts, and come out with $150k in assets with no liabilities. I was always solvent.
This happens daily in the business world’s bankruptcy courts. (Of course some of them are also insolvent)
The math & definitions of solvency & liquidity don't change with scale. They are separate things even if the mechanics of how they influence each other put them in such close proximity to each other that some people confuse the two.
My small scale example illustrated the concept, my large-scale citation of bankruptcy courts show a bit of how it plays out in real life & validates the analogy.