Can I do my Post-doc studies in USA later in my life, or it is no longer an option because I did not complete my present US academic degree?

The rumor you heard is baseless. The only scenario that would affect your ability to re-enter the U.S. for a course of studies is if you lose your visa status but remain in the U.S. without permission of the immigration authorities. You can lose your visa status by accepting unauthorized employment or by losing your current academic enrollment (by reducing your course load below the minimal allowed number of credits, or by dropping out of the program, or by being expelled, or by transferring to another school without adhering to the prescribed procedure). If you leave the U.S. without violating immigration laws, no one would ever care whether you completed the program.