at this time i cant find anything in the code which bans it but, using stranded wire without a fork term. is a bad practice. you really shouldn't need tricks to make a connection to a device. i have yet to see a #12 stranded wire under a device screw that totally held the wire in place. and the very nature of stranded, being flexible, makes the connection easy to loosen from the terminal. if it were me i would either pigtail the stranded wire with solid or use a fork term.
as far as the original question if you look at table 8 in the nec it suggests the opposite of what i thought: dc current resistance is higher for stranded wire vs. solid. solid wire is easier to push short distances (like drops from trunk line runs), and stranded is used for controls.
