2002 Explorer - Fuel Injector Issue

My wife has a 2002 Ford Explorer XLT with 105,000 miles on it. She's been having issues starting it where she needed to trun they 3 - 4 times in order for it to start. We had our mechanic check the vehicle over and said that fuel was bleeding into the engine and that we could replace the injector @ 1,000 dollars or we could turn the key 3 or 4 times to the igniition start position to build enough fuel pressure to start the vehicle. So far this has been working fine. I have 2 questions, 1) does the diagnosis sound accurate? And 2) will the work around of turning the key multiple times damage anything?