Oh, yeah, I've heard that a lot. Some friends of mine went there for swimming in a motorboat.
Also, you may be interested to know that the Colorado River near Yuma has three sections that are all very different, and all are popular with boaters and fisherfolk.
Check the flows here: http://waterdata.usgs.gov/az/nwis/current/?type=flow
Look at the middle column of numbers for the cubic feet per second.
Imperial Dam (Boat launch areas are many, but some examples are Martinez Lake, AZ, Squaw Lake, CA, etc.) So along this above-the-dam stretch (below Palo Verde Dam on the above chart) the water runs very high and deep and fast. It will often run at 11,000 cfs or higher. Today it's at about 10,000 or so. It goes up and down a lot, due to irrigation needs.
Imperial Dam and Laguna Dam is the "old River" area. It is only four miles long, is sort of hidden away, about 10 miles or so north of Yuma. You can get to it from the CA or AZ side. Some of the launch ramps are back on farm roads and you have to ask around where they are. Near Betty's Kitchen there's one, way back in there.
Imperial Dam and Laguna Dam is Mittry Lake, which has many really neat little narrow channels. It's separated from "Old River" by a big levy.
Laguna Dam the river runs again all the way to the Mexican border. It runs past farm fields and through downtown Yuma. Today it is running at less than 500 cfs, which is typical. It is a great place to put in a little johnboat and go fishing. There are many dirt boat ramps amongst the farm fields on both sides, plus a regular ramp at the Yuma city beach park under the freeway bridge, and another ramp at the Yuma city park to the south called "West Wetlands." I do recommend this part of the river. It is uncrowded with speedboats and you will find your little johnboat will do well here in the slower current. There are some very bad sandbars, so you do have to watch it, hopefully your motor will lift up and you can paddle occasionally!