Editorial Comment: 
A question like this raises several thoughts.

First, if a tire is unbranded, how would you know it is Firestone (or any other)? Is it because a salesman told you so, or something external to the tire gave you this information?

If it is a tire which has a similar appearance to the design, but only is marked in small print on the sidewall "made by Firestone", it may not be the same in performance or durability because of differing components which could have been used in its manufacture.

An unbranded tire, is not likely to have the guarantee backing which a branded tire has, even if it is made by a well known company. Any warranty would likely be offered by the retailer, if any.

Finally, false branded tires, have been known to be sold. If you don't know the seller, and you're uncertain about the source, or guarantee of a tire, you're taking a considerable risk in using it.

Tires, because of the vital role they play in controlling your car -- a several thousand pound monster traveling at high speeds, need to be the best quality you can afford if you value the lives and safety of yourself and your passengers.
TG