Another favorite American-perspective truth about Britain I enjoy is when towns in Essex are described as London suburbs. It's inconceivable to me (I lived in Chelmsford for a few years as a teenager) but quite true.
If you mean that it's too far out to be considered a suburb, places even farther out from Los Angeles than Essex is from London are described as suburbs of Los Angeles, so I don't know if it's an American perspective. Apologies if you meant something else.
Typically a suburb is related by function rather than distance. For example I grew up in what's called a "dormitory village" built in Metroland - which is a type of suburb. Like most cities London used to expand by gradually encroaching on surrounding non-urban land - most parts of what we'd now think of as inner London were originally villages on its outskirts, and the city just kept growing. The last batch of growth was "Metroland", the North West expansion of London's underground railway to neighbouring towns last century. And then people said "Enough" and the planning rules were altered to create a "green belt" into which London could not grow. But Metroland is still there, just stuck at the first phase where it's connected to the city but not yet urbanised. You can wake up in your nice cottage amid open countryside in the village of Chesham, walk a few minutes to a London Underground station incongruously sited amidst this setting and travel to your job in the City of London (which you need because a cottage in rural-seeming Chesham is fantastically expensive...). The dormitory villages don't make any sense without the huge city to absorb all these workers, so they're defined by it and by the transport links that make it practical to live in this village yet work in the centre of the city, they are suburbs.
It's not true, though. Those towns have their own history and their own characters. Suburbs are places where housing is built specifically for people who work in the main urban area.