I would read "popular" as "crowded". DH did lap swim at the local public pool for a while, and on Saturdays it was crazy - tons of people. Keeping up wasn't so much an issue as finding space.
However, for stuff like this, I think it's easier to ask forgiveness than permission. Actually, I take that back, I think it's easier to just go swimming, and behave as though anyone who asks you for a doctor's note is nuts. Because they kind of are. They're going to have the lifeguard ask you for a doctor's note? Seriously? Seriously? They think anyone has the time to go bugging their doctor for generic notes authorizing them to go about the normal activities of daily life while pregnant? You don't need a doctor's note to grocery shop, or run after (and carry!) your other kids, or clean your house - higher impact activities in which you are more likely to strain or injure yourself than swimming. Further, it is an affront to your dignity and privacy that you are being asked to provide private medical information to anyone not involved in your care,or to anyone who does not understand the degree of confidentiality such information should be treated with, just so that you can carry on with your daily life.
But on a more practical note, if anyone asks you if you're pregnant, you can always just look offended or grief stricken (take your pick) and say that you're not.
I swam regularly during my last 2 pregnancies at multiple pools and no on ever asked me for "dr's note"
Hmmm... I haven't seen one this pregnancy but this reminded me that my FIL is an MD who has a holistic/homeopathic clinic and is supportive of my decision to UC. He is a bit intense to deal with, but i know he would help out. It would mean going to see him for a visit, though, and it is a 2 hour drive. I will have to think about this one.
you can't call or email and ask him snail mail or email you the note?