I have bought birds three times now. Every time at least one of the newbies gets some kind of sickness. The last time the sick bird nearly died and was in quarantine for two months. Now I get a pair of Hamburgs and the roo is purring and coughing. WTC? Now I have the joy of giving Tylan injections to a full grown Roo with spurs who is wild as a hare. As far as I know there have never been chickens on my property and all the birds have come from established flocks. From now on I'm getting day olds or hatching my own. This is ridiculous.
No, new birds don't always equal sick birds. You've had a run of bad luck. Sometimes stress of the move (from old home to new) brings illnesses out that weren't expressed before.