Chinese Tires??

I just purchased my 3rd Accord, Sliver 04 EX Coupe, Black Leather and XM Radio. Cars has 24,400 miles and I think was a steal at 13,995, however it has a shimmy in front end where you can feel it on the steering wheel but only at low speeds, 40 mph and below. High speeds 50,60 70 mph is fine. I had the wheels balanced but still feel the shimmy. I noticed it has tires I have never heard of "Runway Enduro 606". Could these be the problem? Any suggestions? I figure it's probably NOT mechanical at such low miles?? Will Honda honor the warranty if it is mechanical ?  Thanks in advance..

There has been a recall on some of the chineese made tires in this last week period...check with your dealer on these:
 
                         WheelBrokerAng