'become used to'

Hi everybody,

Does 'become used to' have the same meaning as 'get used to'? I provide the example:

The chief monk, the Venerable Boon Keng, told the BBC that they'd become used to meditating alongside the snake but eventually decided to catch it and take it away to a nearby forest.

It is from a BBC article. 'get used to something' means that (at least in some cases) something is difficult/not normal at the beginnig but it is becoming normal (to the person who does the action) as the time is passing. Maybe I wrote it wrongly grammatically.

Is it the meaning of 'become used to' in this sentence?

The 'Grammar in use' books (and many others) discuss only 'get used to'. I found 'become used to' here:
http://esl.about.com/od/grammarstructures/a/g_usedto.htm

My personal oppinion is that the explanation is not so detailed but the examples suggest that it will be the same as 'get used to'.

Thanks for your help in advance.