It’s hard for me to understand from your thread title whether or not you are serious or not. The post seems to be a parody of its objective, so I will just assume that you are being serious and provide a serious answer in turn.
I don't think it is possible to provide a tidy answer to your question. Presumably there is only anecdotal evidence to go by as I’m sure there haven’t been any published studies on the subject. However, determining the ability of an entire nation to pronounce and speak a particular language better than another nation from hearing just one person speaking seems a little to narrow minded to me.
So in my opinion it’s all relative. Immediately you must consider what constitutes the 'correct' manner of speaking. Whilst technically the notion of perfect grammar is defined in practice, different people will undoubtedly have their own opinions on how tightly or loosely those rules should be applied.
Then you have pronunciation and articulation of the various sounds, once again it depends on how tightly or loosely you want to apply to the technicalities of linguistics.
Every nationality is going to be comprised of sub-cultures with their own grammatical and linguistic skill sets. Whilst the woman you refer to would most likely be classed as a part of the ‘chav’ sub-culture in Britain, you could parallel that with the ‘yobbo’ or ‘ocka’ sub-cultures within Australia. To stick within the context of English, then you will find similar situations in the US or New Zealand. Looking outside of that there is sure to be similar dichotomy occurring within other non-English speaking countries.
So I guess I’m not saying your wrong (although I have a feeling you are), there is just no evidence to support the claim and it would be a hard hypothesis to test statistically.