Would it be possible to have an original Knoll Saarinen chair with Girard Fabric? Or did Knoll have similar striped fabric? I'm guessing that the chair was recovered.

Yes, an original Knoll Saarinen chair could have a cushion upholstered in a Herman Miller fabric - made in the Knoll factory.

This is called COM [Customer's Own Material].

When one orders upholstered furniture from the manufacturer, they usually (but not always) go with a fabric from the furniture manufacturer's collection.

If you look at the listing in a furniture catalog, you will see a line item for the amount of fabric required for the upholstery. Typically, this applies to both the manufacturer's fabric as well as customer supplied fabric. The price of the upholstered piece is usually listed "in muslin" (which is simply the price of the piece, INCLUDING the labor to upholster it, but NOT including the fabric (which could be manufacturer or customer supplied)

Typically, the manufacturer will require his approval prior to using the customer's fabric. This is primarily to insure that the fabric will be physically compatible with the construction of the furniture.