That's a bit of a broad generalization. As with all history it doesn't hold up under scrutiny.
In the 1200s, the empire split into 3 warring countries. The one that took Constantinople was considered the continuation of the Byzantine empire, but maybe it's more correct to think of it as a spiritual successor, than an actual unbroken reign of a single nation.
Which would put it at less than 1000 years of rule. So "a few hundred years" would still be an accurate upper bound.
Even if you take the 1200's as the end of the Empire, and ignore the Roman Republic and take 31 BC as the defacto start of rule of the Roman Emperor, you still are looking at over a millenia.
