Are All Heirloom Varieties Pure Lines?

Question

Are all heirloom varieties also pure lines? The characteristics of a pure line is:

All plants within a pure line has same genotype as the plants from which the pure lines are derived.
The phenotypic differences (variation) within a pure line is environmental and, therefore, non inheritable.
The pure line becomes genetically variable with time, due to mechanical mixture, mutation, etc.

Any thoughts on this? “When I started growing ‘Czech Black’ hot peppers, the fruits varied greatly in shape, from fat peppers with large seed cavities to slender ones with almost no seed. Most were medium-sized fruits that came to a blunt point. If I’d just wanted to save the most seeds with the least amount of work, I could have saved the fat peppers that had the most seeds. But I was trying to produce a seed crop to sell and it needed to be true to the plant type, so I saved seed from the medium-sized peppers growing on the sturdiest, highest-yielding plants. After four years, the peppers were uniform in fruit size and heat – plus, the plants were sturdier and more productive.

Answer 1

Here is an article from Cornell University on heirloom seeds which might answer some of your questions:
http://smallfarms.cornell.edu/2014/07/08/cultivating-the-heirlooms-of-tomorrow/