Sorry to have missed Tim's post.
I have little experience with growing heirlooms, but in my reading I understand that there is a very real problem that we need to be aware of. Same with non-GMO seeds. When heirlooms seeds cross with hybrids, then we have a problem. When non GMO crosses with GMO we have a problem. How easy for this to happen? Unless you are pollinating by hand, blocking off natural pollination, it becomes a very tricky matter even if you are the only one growing things on a large parcel. One has to become knowledgeable in regards to what will pollinate what and how far will there need to be separation. And that is dependent upon variables such as number of insects, their roaming area, and the winds.
Had a friend that was a commercial seed producer. He moved to the area because we were hundreds of miles away from the crops he was growing seeds for. We have all heard the story about the farmers who did not want GMO and ended up in court when Monsanto tested their crop and found it was GMO. We are losing our natural seeds due to this wave of "new seeds". The day is coming when we will want the heirlooms, but we will then have to know how to protect them if we want a second crop. My experience with the heirloom tomatoes is that they are not as easy to grow, and are more susceptible to disease.
Now is the time to learn how to grow them and to protect against cross pollination from hybrids and GMO. The closer you are to other plants that can pollinate, the harder it is to protect your plants.
Runoff from neighboring gardens generally ought not be a problem, unless you are downhill from them. Or in the winter when rain will carry manure a long ways. There is great danger from manure since it often carries the diseases of the animals from which it comes. Cows can transmit e.coli and Mad Cow Disease amongst many others. Sheep and goats can carry Mad Sheep Disease (Scrapie). The reason why it is not safe to eat meat or dairy and eggs is because of the disease in the animals. It is often carried out of the animal through its feces. The last thing we want to come in contact with our food. We see this danger in the spread of e.coli through spinach and lettuce. These are deadly diseases.
We do the best we can. If my neighbor is using manure, then I will have to be extra careful in laying out my garden to avoid his runoff and careful when I work in my garden and harvest my food. We are better off growing our food than buying it, even when it is organic, even when we have these "risks" next door. God will work with us. We are not alone as we try and walk in the light of truth.