We'd always ask other guests around them to verify the story, and then if yes, they were line jumpers, they have to leave without riding. If they want to argue, we can call security -- at which point they usually see the wisdom of just leaving, even if they're complaining at the top of their voices. If they insist that they're going to ride and are making a big deal, we can always not dispatch the coaster (like if they're already on and refusing to get off) -- we can't touch them, but security can. Usually people won't argue too much, no matter how ticked off they are.
Kruggie, I can completely understand you being afraid, because I have been too! I've been physically threatened by guests when trying to make them obey the rules. One really big obnoxious guy was walking through a restricted area on Iron Dragon as a shortcut, and I told him that he'd have to leave the area and go the long way, and he made a fuss. We called security and had them look for the guy, but of course by then he's long gone and they won't find him. It isn't always nice and friendly working at a park like CP when some people think that they're entitled to anything, and it isn't always nice being a guest around those people! But for every jerk there are 999 nice guests that have nothing but great things to say, and it's people like you that make our jobs worthwhile.
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PO!NT OF VIEW - A Different Look at Roller Coasters
http://www.crosswinds.net/~justmayntz/thrills/