Tire Blowout problems of the 2000 Dodge Grand Caravan

I was traveling on the highway at 55 mph with my wife and 3 kids in my 2000 Dodge Grand Caravan. Suddenly the passenger side rear tire blew out and we heard a loud rumbling noise. I was able to cross over 2 lanes to get to an exit without losing control or hitting any other vehicles, my wife and kids were very shook up. After inspecting the blown tire I found 3 seperate slits in the side of the tire were it appeared the sidewall just blew out. I could not find any trace of a nail or any other object in the treads or the sidewall. I brought the tire to national tire and battery and the technician told me that the rim was slightly bent and that this caused the blow out. I am expecting to pay about $135 for the repair, but I have talked with several people who know tires fairly well and they said a slightly bent rim should not have caused this problem. I am more concerned that the other 3 tires may blow at any time and that my family could be at risk. I am asking the technician to check all the tires for any defects after experiencing this, hopefully if there is an issue they will not hide it from me so they can make a profit. I feel like I was very lucky there were no injuries in this case, but I worry about the next time. (tiresize: p215/65r15).