I am in no way a pro, or been hired to do many gigs. Photography is still a hobby of mine, but I would like to voice my opinion...
Where I live, the baseball fields are in a public park. It is not a controlled environment, nor do I know if they have photographers there to even take pictures. However, if they did, I would like to see them try and stop me from taking pictures of my neice or nephew playing a sport!
Everyone here is talking about the "contract"...what about it? The pro-studio signed a contract with the town. I didn't sign anything. That contract has nothing to do with me, with an exception if the contract states that no other photographers can shoot the game. However, it is no longer my problem. It is now the town's responsibility to confront me, not the pro-studio's. If the pro-studio did confront you as you stated, it just shows their lack of respect to another individual. How dare YOU, a photographer, tell ME that I have to leave. it's not your park. You have only ben hired to shoot certain things. This does not make you the owner of the entire field. I didn't sign a contract, and if you did and have exclusive rights, then it's your job to have the TOWN contact me and tell me to stop shooting the event.
Case in point, if they force you to leave or stop taking photos, then they better force every other parent in the stands to keep their camera's home. Just because you own expensive equipment doesn't mean you should be singled out in the crowd, unless ofcourse, it's a controlled environment.
Not to mention the fact that they do not take action shots. I seriously see NO problem in you shooting what you've been shooting, unless the park is a controlled environment (to where you have to have a ticket or pay a fee to enter).
Side note
My cousin recently got married and of course, hired a professional photogrpaher. That same week, I received my 17-40L and wanted to give it a test. So when we got there, the pro-photog was already taking the posed shots. When he was done and the ceremony started, I just gave him a nod of recognition from my seat, of which he returned. I shot the cermony portion without getting in his way. Once inside, during the cocktail hour, I introduced myself to him. He was down to earth and was polite as could be. I flat out told him that if I get in his way, to just let me know and I'll back off. I even asked him if he wanted me to turn my flash off. He said, quite pleasently "Don't worry about it! Shoot to your hearts content. We'll both be fine!"
I got to chat with him a bit more, and he checked out my gear, and I got to check his out. I was stoked! He actually let me hold his Mark II (I think..definitely a Mark, not sure which generation though) with the 70-200 2.8IS and his 40D with the 24-70L. I was in heaven
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My point is, when confronting another photographer, make sure you show them the respect they deserve. Who knows, you could possibly open yourself up to more gigs, or just gain a new friend. I know I did!