Just a student, but honestly I wouldn't sweat it. That's one of those situations where the diverge between the book and real life comes into play. I don't know how your system is, but in mine we board if there is a significant mechanism (i.e. mva) or if the patient complains of head/neck/back trauma or pain; however for, say, a simple fall denying loss of consciousness, hitting the head/neck/back or any pain there, I don't board and collar them. Despite this rule, though, I've had plenty of patients that either didn't want the board or that couldn't or wouldn't have tolerated it. Just do your best and document the hell out of it.
One example I can think of was an elderly patient who fell while outside his house working his house (guy used a walker to get around but didn't have it outside with him) who'd been overcome by the wind and fell against the house hitting his head, had a pretty good gash from it. It was FREEZING outside and raining to boot, and the guy didn't sound like he wanted to come with us. So I walked the patient inside because I'm not going to sit out there watching him freeze and getting him inside and out of the cold where I could assess him was more important than the board. Guy ended up refusing transport despite my best efforts.
Oh, but a little tip one of my classmates shared with me for restraining an intoxicated or otherwise altered patient on an LSB (this is more for physical restraint of a violent patient that you NEED to restrain for your own safety) is to turn the buckles upside of the board/cot upside down. Apparently when the button's not facing up it confuses the hell out of them trying to figure out how to get the belts off.