If your class gives you a choice of skills to be trained in, can you choose a skill you’re already trained in to gain a free skill choice?

I know that if a class would make you trained in a skill you’re already trained in, you can select another skill to become trained in.

My question is about classes that let you pick between certain skills to be trained in, for example the Fighter lets you pick between Acrobatics and Athletics.

If I’m already trained in Athletics because of my background, can I choose Athletics as my Fighter skill, so that I gain another free skill choice, thus having 4+Int skill choices, instead of the usual 3+Int for a Fighter? Or would I be forced to choose Acrobatics?