If company can pick arbitrary locations around the world to be their HQ, or Trump can use Mar-a-Lago as his residence, then so too can every other citizen following the law and paying their taxes.
One is legal the other isn't.... This isn't hard you would be committing fraud no questions. Also depending on how you've lied you'd also be on the hook for tax issues to the government rather then just and issue with your company.
For criminal fraud to happen, there has to be a defrauded party. If I follow my local tax laws and negotiate a better salary with a corporation based on Location A, while potentially living elsewhere at Location B/C/D for prolong periods of time with lower costs of living, that is not fraud.
Getting the company to enter into a contract under false pretenses is fraud. "intent to deceive" is alone enough. This isn't some kind of gotcha where your technically ok if you do X and Y. Intent matters!
Two parties entered a contract with the understand you would live in location A if you don't that's fraud objectively.
