Ummm... no. It was Simpson all the way. Edward VIII could have married her if he accepted it'd be a morganatic marriage, but he wasn't willing to agree to this. His political views weren't all that different to George VI's really- the King after all reportedly wanted to sort out the European crisis in 1939 by going over and talking to Hitler as "one ex-serviceman to another".
The whole Simpson thing was a handy excuse as the establishment didn't like him much, but rumours of pro-fascism weren't the reason for him being pushed.