First of all, there is absolutely nothing shameful in telling people that you got rejected from somewhere. Absolutely nothing! Besides, you will be telling this to someone in the same programme as you - you are on the same level, got into the same school, chose the same school, absolutely 'equal' (if this is what bothers you).
Secondly, if you do want to avoid 'confessing', just say that you only applied to one programme - the one you got accepted to. Very cool, risky, self-confident and somewhat arrogant, no?
Huge congratulations on your offer! Fear nothing and be deservedly proud of your accomplishment!