Ahh but see your post doesn't do anything to help clear up some of those misunderstandings. It would be more helpful to say why a 15a fuse is ok.
And to make sure people understand that over amping a fuse is ok in some circumstances but not in every circumstance...
I was typing on my phone, which is always aggravating, so it was best for me to be brief.
A fuse serves two purposes, the first being protection of the wiring and the equipment from a short to ground, the second being protection of the wiring from "excess amperage" / overload / whatever you want to call it, drawn by equipment; which is what the OP and the first couple posters are concerned with.
In this situation, you are dealing with stout wiring (battery tenders are 16ga, I believe), a very short run of wiring (12" or so), and a specific, known draw on the battery - that being a 12VDC air compressor that probably draws 8 amps or less while running and maybe 10-11 amps on startup (guesses). There is no risk to the wiring melting under these conditions.
If you have concerns about an item "drawing too much power" for the wiring, then I would universally suggest not using it. However, most 12VDC accessories, especially that you might fit to a bike, aren't in any way at risk for that sort of thing. You wouldn't be running an AC invertor with a TV and refrigerator.
I always kind of laugh about fear of 12VDC electricity, it's a docile animal. If you ever wonder "is this wiring adequate", take a look at the factory wiring on your car or bike going to your headlights, which are high amp draws. That wiring will invariably be smaller gauge that that of a battery tender or any other accessory, and it holds up for years, under adverse conditions, and everyday use. Or look at the wiring on the air compressor itself, on mine it is 18 ga wiring, so clearly the unit was designed for even smaller gauge wiring than that and the 18 ga is a "overbuilt" as a failsafe... so the larger 16 ga battery tender lead is actually substantially more than needed.
As per my original post, I have replaced every battery tender lead I have with a 15A fuse, and have run air compressors for years off them and never had an issue. In fact, I only this year got an honest to god pancake style compressor, in years past I used my little bike powered 12VDC model to inflate car tires and the like. None of the wiring is melted, no excess heat noted during use, no blown fuses, etc. The tender wiring continues to also work fine to power my heated vest, and occasional cell phone charge while on a trip, and the actual battery charger. Even if you don't believe my anecdotal evidence, above; believe my actual experiences.