The issue your employer is referring to is nexus or their legal connection to a state. Most states say that if a a company has employees in their state, the employer is required to file an income tax return in that state and allocate income to that state using either 1 factor or 3 factor method, depending on the state.
If you move to ID, it will result in additional tax filing requirements for them. Unless you are a very valuable employee, this may not have a happy ending for your employment status.
This information is based on 36 years as a CPA working in the tax field.
