The Print Statements field (available only with Keystroke Advanced licenses) works with the Accounts Receivable - Print Forms For - Statement Settings when printing Statements for Customers.
If Print Smts is enabled, the Customer's statement is printed when the Print Form For Statement settings "Print Customers Only", "Both Print and Email Customers", and "All Customers" are selected.
If Print Smts is disabled, the Customer's statement is printed when the Print Forms For Statement settings "No Print/Email Customers Only" and "All Customers" are selected.
See:
Customer Database - Main Screen - Email Statements
Customer Database - Main Screen Fields