Sounds a little odd i agree!
Firstly i'm a big supporter of beleiving in your gut feeling and if it fells weird, it's sometimes best to cut and run.
That said you can always ask for more details and if you maybe think there's a reasonable explanation then if your happy with it go ahead.
Maybe ask what they are leaving? give them a list of stuff you'd not allow, (large items, food, animals, drugs ect). Maybe find out why they're looking to leave stuff at an airbnb not a luggage storage place in town?
If they have Gov ID and several reviews on airbnb and it looks like they are a regular user they could just be happy to park and leave valuables out side of a city rather than risk in a car all day, and want to use airbnb as they think it might be safer, won't know unless you get a few more details i guess!