The deadline is the deadline. Oxford and Cambridge post it on the website, and it has been the same deadline for many, many years: before midnight UK time on 15 October. Cambridge is not trying to fake you out by putting false info on their website and there is no secret back channel that will help you. Oxbridge go out of the way to be clear and helpful in all aspects of the application. Perhaps the person you were talking to was thinking about schools that have internal deadlines for their students who are applying to university, to makes sure that everything is done carefully and in good time.
Stop worrying about things you ‘hear’: so far they have not been helpful to you.
ps, I had a student hit ‘submit’ at 11:50pm on the 15th & they got an offer. I do not recommend that approach! nearly killed all of us with the stress…