Bank calling a loan due if I transfer to LLC and if interest rates rise

[Dan N.]

Today in episode 777, David said something very interesting (and frightening) about transferring a property that has a mortgage to an LLC.
He said that if interest rates rise, banks can use certain clauses in the mortgage to call the loan due since they are missing out on higher gains by lending to you instead of lending to someone at a higher rate.
Is this something that happens frequently?
Is there an air-tight method to transfer an investment property with a mortgage from my name to an LLC without having to worry that the bank can call my loan due?