CL65 with ZMA described confused routing event allegedly resulting from ATC mispronouncing and/or misidentifying an intersection; along with the location of same.

Narrative

We were in cruise about 1 hour out of our destination of MBPV. ATC (ZMA) assigned direct SOLEI. A while later; the Controller asked us to confirm we were direct SOLEI; we told him we were. A few minutes after that; ATC said we were south of a direct line to SOLEI and we needed to turn 15 degrees left; so we did. I was then concerned about the integrity of our navigation equipment; so asked the Controller to verify that the LAT/LONG for SOLEI (which was the same on our chart and in our FMS) was correct. I read the LAT/LONG I showed for SOLEI to the Controller. His response was that was incorrect. The Controller then read what he showed as the LAT/LONG for SOLEI. We plugged the LAT/LONG that the Controller gave us and navigated toward it. We were then handed off to MBPV Approach who said after OREDE Intersection proceed to XXXXX. We told the Controller we came in over SOLEI; to which he responded with 'direct' to a different fix. A few minutes later; the MBPV Controller came on and said he talked to ZMA and they had sent us in over OREDE not SOLEI. Now the mess-up was clear to us. ZMA had been saying SOLEI when they meant to communicate OREDE to us. We looked at the LAT/LONG for OREDE and it matched exactly the LAT/LONG that ZMA had given us as the coordinates for SOLEI.