I don't think there is anything rude about applying for the same job that you know someone else is applying for, whether you got the info from that person or from the internet or a search firm. if the job is out there, then anyone can apply for it. If you(in general, job seekers) don't want to mess up your chances of getting a job, then don't talk about it with anyone. it is certainly not rude to say "Oh i don't want to jinx it so i'm not going to say anything", or "sorry, there is a confidentially issue, can't give out more information", or whatever suits your situation.
I don't think "grilling you" is ever polite (unless you're a police officer investigating a crime), but if your friend was asking questions and you were giving info that you didn't want to give - that's really on you. when you are out there job hunting - you need to be careful about what information you give out to people, especially at a time when jobs are hard to come by.
Tinky - your situation is a bit different, because you had to tell her what company /posiiton you were applying for if you wanted to use her as a reference.