Insurance companies do run your credit but the credit check that the insurance companies do is a soft credit check or a soft inquiry on your credit report.
Soft Inquiries do not lower or hurt your credit score or credit rating like hard inquiries do.
Credit card companies and banks or other loan companies do a hard credit check or and put a hard inquiry on your credit report which can temporarily affect and lower your credit score.
The soft inquiries that insurance companies do on your credit do not affect your credit score or credit rating at all.