Why do Vertibirds suddenly appear?

On several occasions while exploring the Commonwealth, a (presumably Brotherhood) Vertibird shows up out of nowhere and engages targets at a nearby location for approximately 5 minutes. Cursory googling only comes up with generic Vertibird information.

1) Are these sequences pre-determined for certain locations? Or is it a random occurrence that can happen anywhere?

2) Is there anything the player can do to influence anything?

3) Will I miss out on anything if I ignore these events and explore the area later? The Vertibird is usually flying around a location I wasn't planning on visiting during the current salvaging expedition.

Solution 1:

1) Are these sequences pre-determined for certain locations? Or is it a random occurrence that can happen anywhere?

No they are not. I've been to Revere Sattelite Array once earlier in the game and fought super mutants there with no BoS in sight. I passed by there a second time once I was further in the story, and a Vertibird showed up there and started fighting the super mutants.

2) Is there anything the player can do to influence anything?

It seems these events start randomly appearing after the Prydwen arrives in the commonwealth. This should occur following the events at Fort Hagen during the reunions questline. It does not seem as though you have to complete either of the quests Reunions or Shadow of Steel for the Vertibirds to appear.

3) Will I miss out on anything if I ignore these events and explore the area later? The Vertibird is usually flying around a location I wasn't planning on visiting during the current salvaging expedition.

Skipping past these events doesn't seem to have any impact. There is no extra loot and they are not part of any missions. The BoS members just show up to battle whatever enemies are in the area. I've seen them fighting raiders and/or super mutants so far.