Pilot reported receiving a low altitude alert from ATC even though they were in compliance with the published segment of the approach.

Narrative

Prior to initiating the approach ATC advised a heavy B767 reported LLWS +/-5kts about 15 minutes before. Approach vectored us to the final approach course from the NE and cleared us for the RNAV X Rwy 17L inside TEBOY. Once established the altitude select was set to 7800 ft. for SEKAW. Aircraft descended and captured 7800 ft. Altitude select was then set for 6900 ft. for BADPE; PM confirmed. Crossing SEKAW; PF selected ALT mode on the autopilot to activate pitch mode. PF acknowledged '6900 ft. altitude armed'; PM confirmed. Shortly after the aircraft started to descend; ATC alerted 'Aircraft X; low altitude alert; check altitude immediately (Low altitude alert alarm heard in background)'. PF and PM confirmed aircraft was at 7100 ft. with altitude alert set to 6900 ft. for BADPE and the altimeter was set to 29.69'. PF noted aircraft was still about 1.5nm from BADPE. PM acknowledged ATC's alert. Moments later the aircraft's TAWS alerted 'Terrain; Terrain; Pull Up; Pull Up'. PF immediately disconnected the autopilot applied power and started climbing. TAWS alerting system immediately disengaged around 7300 ft. PM asked ATC if they could confirm the low altitude alert was no longer a factor. ATC confirmed. At this point the aircraft was beyond BADPE. PF Reengaged the autopilot and set the altitude select to the minimums of 5400 ft. Aircraft broke out of the clouds around 6600 ft. Taxiing into the ramp ATC asked for conditions on the approach. The Captain later recalled an approach they flew into this same airport a short time before. They were following a Citation on the same approach (RNAV X Rwy17L) ahead of them who received the same low altitude alert from ATC. The aircraft DID NOT receive the low altitude alert on this occasion; only the Citation ahead. This may be a common occurrence with the presence of turbulence and LLWS for this approach. Just a half mile from BADPE; terrain is charted at 6146 ft. providing only 754 ft. of clearance from the segmented minimum at 6900 ft. Even with our aircraft at 7100 ft. and 954 ft. of clearance both ATC and the aircraft's TAWS were alerted to low altitude and terrain respectively. That being said; I believe this approach should be looked at and the BADPE intersection revaluated to provide more clearance. This incident nearly resulted in a go around and looking back should have.