That would be a reference to ITA Matrix, an obscure Google tool much used in these parts (and probably nowhere else) to work out fare rules. I too could get it to price up on ITA and what's more it shows the routing rules. It is prices as LON to EWR and back, and allows both a LCY start and EWR destination. So by simply calling up BA you can get that ticket. Mention that ba.com isn't showing this fare, and they should remove the contact centre fee.

But (a) there is always LGW to JFK and (b) though you may prefer to go via Preclearance, I would not say that T5 (or T2 for that matter) to DUB is going to be a poor experience here, particularly as you will be travelling initially as a Common Travel Area passenger. Security queues aren't much different, and the foot leather usage may well be less in T5 and T2 than LCY, given the DUB usual gates in both terminals. Generally speaking Preclearance adds more time than going through EWR as an international arrival since passengers have to front load the contingency.