To answer both sides of this...
Never ever be alone with an athlete, period. It is not appropriate and just shouldn't happen and there should be a rule stating that it can't happen for a lot of reasons. Same sex, different sex, gay, straight it does not matter. You get in to all kinds of area from misconduct to preferential treatment. There is no need for it and shouldn't ever happen.
Phone issue is a different one. I put my phone on to play music and I run a stopwatch on my iPhone. If I am in a lesson and it gets interrupted for any reason I can stop the timer so that I ensure the parent only pays for the time that was actually used. If someone has a 30 minute lesson, I believe they should get 30 minutes of instruction. I will check my phone on breaks occasionally, but if there is an emergency, people that need to know where I am know and they call the gym. Parents you pay a lot of money for your lessons and if you are unhappy in any way with the instructor you have the right and I would certainly expect you to take your money where you are getting the professionalism you expect.