actually, that's easy to explain... the promise is that they
process the petitions in the order in which they were received, not
approve them... think about it for a moment: if they were to APPROVE them in order, one RFE or hiccup with someone from February (or earlier) and the whole process grinds to a halt; everyone after that person would have to wait til the problems were sorted out before they could get their approval... plus think of the extra admin required just to keep them all in order! no, what they promise is that they will start
processing petitions in order, and as far as can be seen, they do this
differences in approval dates come down to all manner of things: one gets an RFE; one needs an extra background check; one has lived in five different countries and looking at all the police reports takes extra time; one has lots of translated documents which need extra scrutiny; who knows...
of course, there's probably some small variation... I can imagine someone going into the mail room, and picking up a stack of ten, with petitions say from May 23... that person goes back to their desk and puts those ten down, and starts working through them in order
the next adjudicator might go in half an hour later, and also get a stack of ten, maybe from May 24... but of course when s/he starts working, his/her first one will be later than the one at the bottom of the first adjudicator's pile, which might have to wait an extra day or two

(mind you this is just me imagining; I have no idea if it happens this way or not

)
in any case, it's NOT a 'straight-up lie', you just misread/misunderstood what their promise means