Corporate aircraft cleared for ILS/LOC Rwy 2 approach to SAF routed via V611; transitions to IAF and initiates a descent and was advised by ATC that he/she should have remained on airway to complete the ILS.

Narrative

En route to SAF and just north of ABQ we were rerouted by ATC direct NELGE intersection then Victor 611 for the ILS Runway 2 in SAF. Just prior to NELGE we were given a descent to 9000 (MSA is 10;400). We assumed that the clearance was to join the ILS at and IAF along the airway because there is no transition or feeder route from the Santa Fe VOR to an IAF on the ILS Runway 2 approach. Victor 611 shares a fix that is an IAF for the ILS 2 approach (LIYIR is the name of the fix I believe). So we proceeded to this fix and joined the ILS. Prior to the IAF we were told by ATC to maintain 9000 till established and cleared for the approach. Once we had started the approach (just inside the IAF) the controller called and said that we were supposed to be on Victor 611 and that the MSA in our sector was 9;800 (we were 800 feet below the MSA). This call occurred about the time we were joining the localizer. We saw no conflicts on the EGPWS and remained at 9000 to capture the glideslope and flew the approach to a landing. There was ambiguous verbiage provided by the controller. Because there is no transition on from the SAF VOR to the approach we believed his intentions were for us to join the approach at the IAF which was on the airway. We assumed that he had descended us to a lower than published altitude that safely met his Minimum Vectoring Altitude. We should have queried the controller about the altitude. The controller should have cleared us to an Initial Approach Fix and then cleared us for the approach; which is what we assumed he was doing but were evidently incorrect. This confusion placed our aircraft 800 below the MSA.