In this day and age, old employers don’t give ANY info to new employers. This leeway should work to your advantage.
Think of all the things, even tiny things if nothing else, that old employer might not have liked. Perhaps things beyond your control - project nearing completion? department over budget? Imagine a prospective new employer hearing these rationales - a good new employer will understand old employer’s trials and tribulations of budgeting, staffing, and so on... especially for contract workers, where no reason to terminate is required.
You're absolutely right. I worked in HR for almost 35 years and while we did verify employment, we only verified dates of employment and position held.
As a side note, we've had skilled tradesmen who were a real pain in the butt get laid off and were successful in applying for a position with the big three. There was no way we wanted to inhibit the guy's chance in getting hired with them since we knew that he wouldn't want to leave that job if we called him back to work.........LOL!