Yes, you can use your brother's "extra" receiver. DirecTV has no way of knowing where that receiver is, unless you plug it into a phone line. Leave it plugged into the phone line at the brothers house, but keep it unplugged while camping. The Sat service is one way, so they can't tell.
Now, if your personal ethics stop you from doing this, well, that's a different problem that I'm not qualified to help with.
2000 Excursion Limited 7.3 PowerStroke 3.73 gears
1993 E-350 Super Club Wagon 351W, E4OD, 4.11 LS rear (named Clifford)(Retired)
2010 Salem 30QBSS
1 DW, 1 DD, 3xDS's