They do have flash on fabric, but are they true flash based logic remains unknown to me. I used proasic3, and I can say that proasic3, igloo, fusion devices are flash based logic.
Altera MAX 10 has on-chip configuration Flash in addition to User accessable Flash blocks, according to the family datasheet. Some devices have even two configuration block to allow live configuration update. As far as I can read the datasheet, the devices are not hot at power-up, ie. it takes a few milliseconds from the device to read its on-chip configuration Flash and configure its logic fabric, and this needs to be taken into account on the system design.
Altera's solution is quite similar to Xlinx's and others SRAM-based logic fabrics, except that the device contains one-time-programmable configuration memory, but it can also boot from the external SPI Flash memory similar to Xilinx and others.
Microsemi's Proasic3, Igloo and Fusion devices are hot at power-up AFAIK ie. the device configuration is stored at the logic elements thus eliminating those a few milliseconds and the device is ready to rock&roll as soon asi it will be powered up.