Final answer:
The statement is true; American colonists objected to the lack of representation in the Parliament that levied taxes on them, summarized by the phrase 'no taxation without representation', not to the principle of taxation itself.
Step-by-step explanation:
The statement that the colonists did not necessarily object to the principle of taxation, but rather how the tax money would be applied is True. The dissatisfaction among the American colonists was not primarily about the taxes themselves but about their lack of representation in the Parliament that levied these taxes. This sentiment was famously summed up in the phrase 'no taxation without representation.' The colonists felt that it was unfair for them to be taxed by a government in which they had no voice or vote. As such, the objection was more about the governing process and the use of the tax revenues, rather than the concept of taxation.