Actually, non-native speaking airlines do have translators on board. They are not usually pilots. The new standards do say that having translators in the tower or in the cockpit does not mean the actual operator of either can have lower than level four proficiency.
I have heard of incidents and/or accidents (can't think of any at the moment) that have occured due to the fact that these translators are not able to understand operations and mistranslate.
It is very likely that you were talking to one of these translators.
Just last week a friend of mine returned from a flight and said that he asked for something that there is no R/T and the ATC said "standby". About 3-4 minutes later a different voice (original ATC was male the next voice was female) asking to repeat. This person was not an ATC it was obvious she was there translating every word.
PE