have/has in respectable media

This is just for my edification, not a teachers tip or anything.

Surely the following sentence should be 'have' not 'has'...
Analysts say currency controls that restrict the availability of dollars for imports has played a key role in creating the scarcity of many items.

I know there is an 'over the pond' difference in have or has usage but this doesnt apply here as the only word to use is 'controls', which is objectively plural to my non-grammatically trained, but advancd level of experience in 'right propa good English, like'

Im posting as this sentence was on the BBC news website, I've seen loads of crap grammar on there recently and wasn't sure if this this is wrong or I'm losing my sense after being in China so long....because that happens!

I might even start calling the 'bus' the 'bas' soon.....

Yes.  Because "controls" are plural, and the verb refers to them, it should be "have". 

But it is also possible to look at the clause "currency controls that restrict the availability of dollars for imports" as singular... as "a" specific thing which has had the impact. The plural within the clause does not in itself make the clause plural where it is referring to one thing.

I think it does actually depend upon how you break up the sentence which determines which is correct in this case.

To me it can certainly be correct as it is.  (But also potentially correct in the plural form.... There is just a slightly different meaning in interpreting the meaning of the sentence in each case).

Analysts say "A" has played a key role in creating the scarcity of many items. Where A = "currency controls that restrict the availability of dollars for imports"

After reading this, I has got a headache.