I don't think so. After training all summer for soccer last year, I went into preseason and ruptured my lung. I was in the hospital for a couple of days and my heart rate was typically the fourties. For the two nights that I wasn't in the ER, I was woken up 6-7 times by the nurses (even though the doctor told them not to at the begining of their shift).
I had to walk around because my heart rate was going as low as 31 bpm when sleeping and they thought I was going into cardiac arrest (even though the aforementioned doctor told them otherwise - I was just in great cardiovascular shape).
After that, I started focusing on lifting. When I wake up now, my heart rate is around 55 bpm. I definately think it has to do with fitness and believe Lance's was in the low thirties.