Is it true that if my baby can bend his finger or toe, it isn't broken?

No. Sometimes babies can bend digits that are broken, and sometimes won't bend digits that are not broken. Unfortunately, sometimes x-ray studies are needed to determine if bones are broken.
No. A broken/fractured digit on foot or hand can still be moved, usually with more pain. If you suspect a fracture suggest it gets checked.
Not at all... You can move an area with a broken bone. There will be increased pain, but it doesn't "self-splint" and stop moving.
No. No! a bone can be broken, but the muscles and tendons still work...Often a child will hold a broken bone still to protect it or prevent pain, but being able to move it is not a good test for fracture. Broken bones usually cause swelling and localized pain, but check with a doctor to be sure.
No. Babies have lots of flexibility. Being able to bend a baby's finger or toe does not confirm that the finger or toe is unbroken. The doctor will also assess the amount of trauma (type of accident), the amount of pain on exam, and the amount of swelling. Also, x-rays may be needed.
No. This is not a reliable idea. If everything around the break is intact, muscle, tendon, and ligaments, the finger or toe may work well but still be fractured (broken).