Definitely not a Ficus. There is a reason why you have never seen a Ficus with visible flowers, and that is that the flowers are tiny and are concealed inside the fig or syconium. In most Figs (except those that are parthenocarpic) the flowers are pollinated by a host specific species of wasp which gains access to the syconium through a small, natural opening called an ostiole. Figs and fig wasps have a very fascinating symbiotic relationship.
Very interesting info, Darwinensis. Never knew. The thing that made me think F.elastica, was simply the shape and possible size of the leaves. Having said that, I'm thinking Rlalique could be on to something here.
You're right about the petal count so it's not Ixora. The "oppositifolia" of the OP's plant does kinda show that alternating opposite leaf arrangement. I was just trying to figure out if the bloom itself is right (centre).