Your key words are "least likely".  Nothing is 100% safe.
Probably the safest source are just hatched chicks from a reputable hatchery, one that have been in business for a lot of years.  They take biosecurity seriously or they would not still be in business.
Matek's cannot be passed down through hatching eggs but I'm not sure about that concerning bird flu.  Still, I'd consider hatching eggs really safe.
Chicks from a feed store come straight from the major hatcheries so they are very safe.  But you have people walking around those feed stores that could be contaminated.  That's why they are third on my list.  Still, I'd consider them very safe.
Now we get to what I think you are mostly interested in, getting older females from neighbors.  Any flock, including yours, can have flock immunities.  That means they have the disease and can pass it on to a new chicken but each member has developed an immunity to it so you will never see it.  A good example is Coccidiosis.  Many flocks are infested with the bug that causes Coccidiosis but they develop an immunity as they grow up.  Yours could easily give something to new birds.  But I don't think Marek's or bird flu operate that way.  They may have an immunity (many do to Marek's) but I think you would see some results if the person you are getting them from is honest and tells you.  I think they would know.
The biggest danger is from recent exposure.  If the flock has recently been exposed to one of those diseases they may not have had time to develop symptoms.  That's one reason birds from a chicken swap or market or auction are such a great risk, they are exposed to a lot of strange chickens just before you bring them home. 
To me, the safest older birds to bring home are from a closed flock. one that has not had any exposure to strange chickens for over a month.  I cannot guarantee that they are safe, just the safest.
Those stories are real.  The established commercial operations are not the ones in those stories.  They do not introduce new chickens to their flock, but clean out the entire flock and sanitize when it is time to replace their flock.  They are not going to take the chance of wiping out a flock of thousands by introducing new chickens.  If they get bird flu it is from other sources.  Often wild birds.
Backyard people do sometimes introduce diseases and parasites when they bring in outside chickens.  People do this all of the time and it is often not a problem.  When they do bring something in it is usually something fairly minor, a parasite or something easily treated.  More of an inconvenience than a disaster.  But it is certainly possible you could bring in something that wipes out your flock. 
I agree with 
@aart   What are you seeing that makes you want to do this?  How old are they?  How many do you have and what do your facilities look like? 
If you want more eggs or more hens anyway, fine.  That is legitimate.  But if you want to change a cockerel or rooster's behavior, lets discuss it.  There may be other solutions.  Often adding more girls does not change the behavior but gives you the additional problem of having to integrate more chickens on top of the other problems.