While mapping out some remote tours a few times, I think it would be handy to have the ability for Basecamp to find POIs, such as petrol stations, that run along your route within a range that you specify (such as 2, 3, 4 miles...). That way I won't have to locate and map them myself using the find feature.
While we are always trying to improve our user experience, there may be a work-around for you.
You might use the trip planner feature. There is a search along route feature included with that. A search for fuel stops will yield results. Does this help you?