Nobody is asking you to lie. The guidance about not referencing how you found them means don't open by naming their default, because that lands as surveillance and ends the call. If they ask directly, you tell them the truth: the filing is a public record and you watch public records for houses to buy.
A workable opening is short and about you, not about their crisis. Something close to: my name is X, I buy houses in this area, I know this may be a bad time, is your house something you'd consider selling? Then stop talking. Their answer tells you whether they're in denial, already working with the bank, or relieved someone called.
What makes this work isn't the script, it's that you can actually do something for them. An owner with 40,000 in equity and an auction in ten weeks loses all of it if the sale happens. You're offering to pay off the lender and hand them the remainder. If your version of the offer doesn't leave them better off than the auction does, no amount of warmth in the opening saves it.
One thing to prepare for before your first call: a good number of the people you reach don't want to sell and are trying to reinstate the loan. The professional move is to say so, wish them well, and note the date to check back, because roughly speaking most attempts to cure a default don't get all the way there. Also confirm what your state and the federal rules require about calling numbers on the do-not-call registry, in writing, before you dial a skip-traced list.