I don't doubt their sincerity (unless they were just trying to get rid of your salesman!), but I don't agree with their understanding of faith and the ways God may use to take care of them.
It's true that God has promised to take care of those who depend on Him and trust Him to provide for their needs. But God hasn't promised that we'll never be sick or have accidents or experience disasters or eventually die. Nor does it mean we shouldn't save money or use common sense to prepare for such things (either to prevent them or recover from them). The Bible says, "The plans of the diligent lead to profit as surely as haste leads to poverty" (Proverbs 21:5).
Refusing to plan ahead and provide for the future is neither wise nor prudent, and I believe insurance can be part of these plans. If we don't prepare, someone will still have to pay if disaster strikes, such as a relative or some other person.
At the same time, we must never forget that life is uncertain, and the greatest preparation we can make for life's surprises is to put ourselves into God's hands. He loves us, and even in the midst of life's greatest trials He will never abandon us. Make sure of your commitment to Christ, and learn to face life's trials with trust and with faith. Jesus' words are true: "Surely I am with you always, to the very end of the age" (Matthew 28:20).