No. The one-person bird is a real phenomenon, but it belongs to the parrot world, where a hand-reared cockatoo or African grey may pour all its social devotion into a single human and treat everyone else as an intruder. A zebra finch's social wiring points somewhere else entirely: at other zebra finches. Understanding that difference saves new owners a lot of misplaced hurt feelings.
Where a finch's loyalty actually sits
In the wild, zebra finches live in flocks in the Australian grasslands, and a cage pair keeps the same instincts. Your finches will feed beak to beak, preen each other's head feathers — a liberty they allow only a trusted partner — and sleep pressed flank to flank on the same perch. That is where their attachment lives. You are part of the scenery: a predictable, mostly welcome part, associated with seed, greens and bath water, but not a member of the flock and never a rival for a finch's affections.
Why nobody in the house gets chosen — or rejected
Because finches do not bond to individuals, they also do not play favourites among people. The finch that panics when you reach in to change a perch will panic exactly the same way for your partner, your teenager or your house-sitter; it is reacting to a hand in its territory, not voting against you personally. The calmer side of the same coin is that a finch which grows relaxed about one person's presence — perching near the bars while someone reads beside the cage — extends that tolerance to anyone who moves quietly and keeps a similar routine. Time spent near the cage earns trust in the species generally, not devotion to one keeper.
The exception owners sometimes misread
A hand-reared finch, or one raised alone after losing its mate, can become unusually focused on people: following movement along the bars, calling when the room empties. That is not a one-person bond forming — it is a flock animal missing company, and the kindest fix is another finch, not more human attention. Similarly, a male singing persistently at one household member is usually singing at his own reflection in a nearby object or simply courting the world at large. Read finch behaviour through the flock, and it stops looking like favouritism.
What this means for a shared household
Practically, finches are one of the fairest pets a family can keep. Every member can take turns with the morning seed and evening greens, every member gets the same cheerful beeping greeting — which is to say, the greeting the flock gives the day itself — and no one is bitten for being the wrong human, as happens with bonded parrots. Consistency is the only thing to organise: the same seed mix, the same lights-out time, the same approach at the cage. For that shared routine, relatives you pick can themselves look at the profile you keep for the flock once you grant them access via KinsLe's Family Sharing, rather than rely on information relayed around the house.