I don’t know about the phone calls, but the stress card thing is nonsense. A long-standing rumor based off a proposal that was never actually implemented. At most, cards were handed out with contact information for help if recruits were considering doing something really stupid like going AWOL or attempting suicide (which they do).
A friend of my sons, actually his best friend went into the Army while my son went to the Marine Corps and his friend said that they are given stress cards too