This is not intended to agree or disagree with any NASI initiative. It adresses specifically the notion that people are rightfully suspicious and cynical whenever anything is attributed to gedolim. I cant speak for other people and their motivations, but I will tell you my reason.
If the Gedolim truly believe what is attributed to them, why dont they come out and say it? I am a close talmid of one of the signatories on the original NASI initiative, he told me straight out that what he was told and what the add says are not the same thing. He was asked if he would sign that it is a good idea to promote close in age shidduchim. He responded yes. The resulting ads then ran with a whole discussion on age gaps and claims about girls never marrying… oh and by the way we think people should promote close in age shidduchim (more like getting a signature and then adding text). I am also personally aware of someone who sent a letter to Rav Chaim Kanievsky Shlita asking him if what was reported in his name (the specific issue is irrelevent here) as well as his fathers name was true. I saw the reply, it contained two words “Lo Hadam”. People do have every right to be cynical about things reported in the name of a gadol or gedolim, nobody knows what the question was or what the answer was, all we know is that someone claims this is what he said and this is what he meant. In the case of the NASI ad, not only has this Rosh Yeshiva not encouraged his own bachurim to do close in age shidduchim (he wont discourage it), one of his own daughters got engaged and married after the appearance of this ad to a boy more than 3 years older than her (she was almsot 20). In short, things that are verifiable often dont hold up to scrutiny, so am cynical and often simply do not believe what was said in the name of any gedolim.