Absolutely you do! We used Carrara marble, and it is flush. Our builder had to search a little to find the thin slabs...but it CAN be done! My neighbor used slate, and hers is flush, too.

Here is my FP...

And here is a little bit closer shot...

Yes you should be able to get it...we got a one piece marble (same slab used in the surround) and it sits flush with the flooring.

If it can't be done for whatever reason, then you should be able to get a carpenter to make a wooden bevel to match your flooring as a transition piece so you won't trip or whack your toes. We have slate flooring under our wood stove and the mason put a bevel on the edge of the slate to prevent just that.

We went with granite--I found a remnant that I loved, in a size that would work, and for a really good price. As the granite is thicker than the hardwood, the hearth sits slightly above the hardwoods and has a beveled edge. We have not had any problems with tripping and I attribute that to the beveled edge. Another option if you go with granite is to go with the thinner grade.

Here's a pic of ours:

Hope this helps!