YES! 3rd party processing can isolate you from your customers at the cost of effective business relations. Depending on your size, projected gross sales, tax liabilities, you are going to need records of transactions. The more detailed those records the easier your compliance becomes. While you are not the direct card processor, oversight is necessary to protect your ‘good’ name.
Don’t think of the relationship between you and your processor as being ‘set and forget’. Track failed sales and chargebacks.