You are right, I thought about it more on my commute today. I actually disengage the right cleat first, then stand up (i.e. lift off the saddle) and start braking, and last lean to the right and put my right foot on the ground. Its hard to put it in writing, but my point was that the feet are not supposed to touch the ground while seated.
The OP also needs to be sure the bike is checked for assembly defects in view of her initial problem with the handlebars being loose. Based on this problem, I am guessing the bike was purchased either used, at a dept. store, or poor quality bike shop.
While many shops will charge $100 for a 'pro-fit' the OP may be able to find a shop that will give the bike a going over, and check her set-up (saddle, cleat, and bar position) for less than that, especially if they are trying to aquire a new customer.
*hangs head in shame* I got it for $86 at Toys 'R Us. My dad got took real bad at a bike shop, so when it was time for mine and I was testing the waters as to whether this was my thing or not, I opted for an el cheapo from Toys 'R Us, with the plans of getting a better bike when my bank account allows. I just discovered a bike shop locally that has been getting rave reviews and hasn't been there long, so I'll probably stop by, with the bike, on Sunday to have them give me an assessment, and if they seem ok, I'll eventually be buying a better bike from them.