It might be similar to a Motte and Bailey Fallacy. Though that one is more focused on distinct but related definitions than it is for distinct but related situations. Not the exact one that you are looking for, but the related concepts might be a path towards an answer.
You don’t necessarily need to roleplay, but something like “I would like to play on their guilt by seeming hopeless.” or “I would like to bring up the horrible acts of the orc warlord to stoke their anger.” or “I would like to convince them to help by pointing out how their oaths may apply in this situation.” would really help sell the specifics. If you are just trying a flat check I have no real way to know what you are planning on doing other than just sort of charmingly asking “Please?”
“Most consumers want fast food companies to label when sawdust has been added to food - but trust restaurants less when they do.”
Even without a gameboard, and even without finely tracking movement at all, you can still have players with movement builds and make them feel powerful. Describing opponents like longbow users and warmages as being within range of a move action “for you, but not for the others” is just one basic way to make them feel fast. Things like difficult terrain being an effective nonissue for them is good to keep in mind. Just remember to describe how fast they are in combat, and give them fun things to do with that speed.
The trouble with ‘Slippery Slope’ and ‘No True Scotsman’ is that they themselves are not fallacies. Invoking them without proper justification is the fallacy. The same sort of thing happens all the time with ‘Appeal to Authority’, you can probably trust a scientific consensus about a subject in which they are all experts, but you probably shouldn’t trust an individual expert on a topic for which they are not recognized as an expert.
For an example of Slippery Slope: Fascists will absolutely try to demonize the most available target, and then because they always need an out-group, they continue cutting at what they consider the ‘degenerates’ of society until they are all that remain. (And then they find some new definition of degenerate)
“No True Scotsman” is valid in that there is at some point by definition after which you are no longer talking about something. “No true vegetarian eats meat” is valid, as this is definitional. “No true member of Vegetarians United eats meat” lacks proper justification, and refers to an organization, not a proper definition. This gets really messy when people conflate what group people are in with what they ‘are’ or what makes them a good example of a group. Especially when religion is involved.
I imagine if my occupation includes carrying a gun, interacting with citizens, and a historically high rate of extrajudicial deaths amongst people I am supposed to be protecting. A publicly accessible camera would be beneficial to easing the minds of those I interact with and providing evidence for any actual instances where I felt my life was threatened.