From an “old hand” The Locum Agency need a fee to make a living.
Always ask yourself for whom the Locum Agency works? Who is paying their fee? You or the employing practice? Therein lies the answer as to whom they are loyal.
Its just like any other Agency eg an Estate Agent, or a Travel Agent. If you are paying the fee they are loyal to you. If another party is paying the fee they are loyal to them.
I hope you are successful in your decision to work for independents. It is a much better working environment and you will be more ethically focused rather than target focused. And the other advantage is you know who the boss is and if he/she is one of the many DOs who now own practices you will be working alongside him/her and any grievances can be aired and quickly resolved.