cooperplace,
I used to fly this trip at the Bar 10 about 18 years ago. It was a favorite job for us pilots; and the Bar 10 folks were some of the nicest people I ever met in my life. Some things may have changed since then, but I suspect very little has.
If you think back you'll probably realize that you weren't just low, you were close to the canyon walls (both the Grand Canyon and the smaller side canyons leading up to the Bar 10 airstrip), probably on the right-hand side. The reasons for this are:
1. In my time we usually ran this operation with two B206B's. When one was on the ground (sandbar on the river shore) at the bottom of the Grand Canyon, picking you up, the other one should be on the ground at the Bar 10 ranch, dropping the passengers he'd picked up 8 minutes earlier, and vice versa. So during the trip between the ranch and the river you'd meet somewhere, head-on. To avoid Bad Things Happening, besides co-ordinating our movements by radio contact, we'd both keep to the right side of the canyon for lateral separation.
2. There were no safe places to land, even fully under control, between the sandbank where you were picked up and the start of the airstrip. Helicopters need a level place to land or they'll roll over; the whole area between the end of the airstrip and the river is one big slope, varying between steep and sheer. If you'd try and land here the rollover would probably only end on arrival at the river. So if the engine quits while climbing up these side canyons your only chance is to turn around immediately to try an autorotation glide down to a sandbar at the river shore. You need room to turn around, you make that room by remaining to the side of the canyon.
There were some other considerations to do with avoiding abusing the Grand Cayon SFRA rules and keeping the noise localized but they were secondary.
And with the above reasons why one should fly low, one cannot disagree with Georg1na and diginagain...