Yes, those tires are too big for the stock wheels.
Here's the recommended sizes. Stock wheels are 9'' wide.
Recommended 20" tires for 2010 Camaro
245/45-20 = 28.7" tall, 8.0-8.5 wheel
255/45-20 = 29.0" tall, 8.0-8.5 wheel
265/40-20 = 28.4" tall, 8.5-9.0 wheel
275/40-20 = 28.7" tall, 9.0-9.5 wheel
285/40-20 = 28.9" tall, 9.0-10.0 wheel
295/35-20 = 28.1" tall, 9.5-10.5 wheel
305/35-20 = 28.4" tall, 10.0-10.5 wheel
315/35-20 = 28.7" tall, 10.5-11.0 wheel
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