Final answer:
The statement is true; colonists objected to the British tax policies primarily because they lacked representation in Parliament to influence how taxes were used.
Step-by-step explanation:
The statement that colonists did not necessarily object to the principle of taxation, but rather to how the tax money would be applied, is true. During the period leading up to the American Revolution, many colonists were upset with British tax policies, not solely because they were being taxed, but more so because they had no direct representation in the Parliament that was passing those taxes. This sentiment is encapsulated in the famous phrase 'no taxation without representation', which highlighted their primary grievance of not having a say in how the tax revenues would be utilized.