If they aren't planning to do something illegal, then the threat doesn't apply to them. Are you just arguing that the BBC is doing sloppy writing here? Here's some more examples that have the explicit language you seem to be looking for.

https://www.theepochtimes.com/migrant-caravans-prove-a-succe...

- has multiple specific examples

https://www.washingtonpost.com/world/at-the-us-border-migran...

>The caravan also includes single men who say they will attempt to cross the border illegally and others who plan to stay in Mexico.

https://www.usatoday.com/story/news/world/2018/11/09/migrant...

> but 122 quit waiting and entered the country illegally to request asylum, according to data from U.S. Citizenship and Immigration Services.

https://www.washingtontimes.com/news/2018/nov/28/migrant-car...

“The standard wisdom [that] it’s all about violence could not be supported by our data,” said Detlof von Winterfeldt, a researcher at CREATE.