Can a member come just to walk or must pay special program ticket each time?

There is admission fee

If you're a member of this or other participating botanical garden society, you can visit for 'free since a membership to participating society is required

I'm slightly confused at the question. As a member you will can enter the main grounds for free. There are some interior exhibits and special events that require a member to pay an additional charge. The above ONLY applies if you are a member.