Should I be truthful about graduate school rejections?
As someone involved in graduate admissions decisions, I can say unequivocally that knowing a student has been denied admission at another program does not negatively influence my admissions decisions.  I have all of the application materials from the student, and (assuming the applicant is strong) the decision is sufficiently important that I will certainly look at and evaluate all those materials.  The decision of another school is not a useful indicator of whether I should admit you.

Indeed, if you tell me you have an offer from another top program, I might even be more cautious about offering you admission.  Why?  If I make all my initial offers to students who end up going to other schools, then I have to go back and dig through the applications and find the ones that didn't already accept an offer, which by that time will be lower quality applicants.  I know of one program where this happened last year and they resolved to make more strong offers to the second tier of (still quite strong) applicants this year.