As you come in on the Ranger on Tuesday, extended Labor Day weekend visitors are already "bedded down" at rock, getting poised to board the Ranger at 9am wednesday to leave the island, even though very few people really ever want to leave the island (sort of the opposite of "Lost").
So it's either travel 3 miles to 3Mile campground, where u are likely to get one of the 8 shelters there (but no guarantee, as some folks hike into rock from there to catch the Ranger's departure in time), or take down the tent at Rock (ugh!). You could go on a "water run" (hey, turning on the spicket at the campground is hard work!), while your "better half" tackles the tent tear-down.
Take solace, however, as even if the tent is wet, it'll be no big deal. Folks (those leaving on the Ranger) will clear the shelters at Rock by 8 am or shortly thereafter. Bring along a light rope, string it inside the shelter, and let your tent dry while u guys are off doing whatever. This can now be "home" until u leave.
When someone occupies a shelter, they attach their 4 x 5 1/2" white backcountry permit (enclosed in ziploc bag)[provided] using a long red twist tie [provided], to the outside handle of the full-size screen door of the shelter. NOBODY will walk into your shelter when you are gone (except perhaps a ranger upon reasonable suspicion that there is something amiss).
The shelters are set back a bit from the trail. After Labor Day, NOBODY will even approach the door or front screen of your shelter, as the permit hanging on the door handle tells them it is occupied. I suppose someone could check out the permit if they were anticipating a rendezvous with another party, and wanted to check if it was indeed their friend(s).
Before Labor Day, someone might approach your shelter (especially at RH or 3Mile, where the camp limit is 1 consecutive night) to examine your stated itinerary (as shown on the permit) to figure out if you already stayed your 1 nite, and are likely to vacate the shelter later in the day.
NOBODY, including professional thieves, comes to Isle Royale to steal. The transportation (and time) cost to get to the park cuts into any $ to be made separating people from their property.
Whenever I visit, and often stay in a shelter, all of my gear is spread out on the shelter floor. Luckily, so far I have not had a problem. Though perhaps I am a bit naive and too trusting. I do, however make a point of not leaving my water filter conspicuously hanging inside the shelter screen, just for good measure, i suppose. And i usually take it with me on dayhikes anyway. I have the old Katadyn pump (made by Pur)(weighs 14 oz and kinda bulky)(can't wait to get the 3 oz Sawyer filter!!!!!).
RH, while not the ideal base camp, will afford you the opportunity to do a one-day canoe rental to accomplish 2 things: 1) paddle from the seaplane dock straight across Tobin Harbor, then hike to Lookout Louise (if the lake cooperates, u could paddle to the Hidden Lake/Lookout Louise trailhead down Tobin Harbor a mile or so); 2) explore the far western end of Tobin Harbor-very nice!
Rent the canoe right early in your trip. Boat, kayak and canoe rentals will be closing for the season shortly after your arrival. Make a point of asking when they plan to close, once you get off the Ranger (the rental person is right there, next to the same boat dock where you disembark upon arrival to the park).