Go to any of these, and order Hong Kong noodles. Go another day and order Singapore noodles. There's a high chance you will get the same thing. I asked the chef (A cantonese) at a RedHill shop why the Hong Kong mee is called Singapore noodles and he told me that the noodles were being cooked in Singapore, so why call it HongKong noodles?
The cantonese took the foods from the different cultures they met and made it their own. They moved to other countries and it becomes associated with the new country. Case in point being Hainanese chicken rice, made famous in Singapore with roots in Hainan. Curry was just another spice they incorporated into their repertoire. Also, by using the words Madras Curry Powder, it would be more easily understood by Western readers. What if they had used the red African curry powder also available in USA?
Migration of humans and food have happened throughout history, some recorded and some not. Take for example fish sauce originating from China and made famous by the Thais. Another would be Catherine De Medici from Italy kicking off French cuisine like we know it today by introducing techniques and foods such as truffles and quenelles to the French. The former was unrecorded, but the latter was.
So who's to say Singapore noodles is not a cantonese dish? Sure as heck all the chefs here that cook them are cantonese. Maybe it was made famous here. Let the people in HongKong throw their jokes. Between Hong Kong noodles and Singapore noodles, which one appears in cookbooks more and is more likely to be recognized by westerners (Eileen Yin Fei Lo's Chinese Kitchen book has Singapore noodles too)?
I'd say Singapore got the last laugh, because we stole their recipe and made it ours. And yes, I've tasted fish sauce in some Singapore noodles too. Does that make it any less authentic?
Who cares, as long as it tastes good right?