Some folks are even against crossing different lines of Buckeyes (called outcrossing). In other words, they do not believe you should cross a Buckeye into your line if not from your strain. I have found this NOT to be true. If another Buckeye line has something you need in your line, it can be beneficial to your line. Most lines go back to Urch anyway or has Urch introduced into their line at some point in the past so never really a true outcross.
What you are referring to when another breed, such as Cornish or Barred Rock, is crossed into the Buckeye to accomplish some improvement in a trait or traits is called grading (aka cross-breeding). I am OK with grading if the breeder does it correctly, and I think it should be done only when a particular trait cannot be improved by good breeding within the breed. There are many examples of breeds being messed up because of irresponsible grading but a lot of those were folks toying with the foundation breeds.
The Buckeye is a composite breed. If you choose to cross-breed, that you use one of the breeds used to originally make the breed.
Composite breeds are those that have been developed from the original foundation breeds or other composite breeds. Theoretically, if a composite breed went extinct, you would be able to re-create the breed using the breeds used to originally make it. If a Foundation breed disappeared, its genes would be forever lost. There are also some very old composite breeds that people are just not sure how they were created.