There isn't a lot of good data on foreign transactions because regional and federal governments have worked hard to make sure data was not collected on it. Popular pressure is slowly changing that.
One observation I have is that even if it's just single digit as a %, it can exert very significant pressure on the market. A bubble is a mob effect. It begins with some properties purchased at prices the local market can't support, regional opportunists jump in seeing the opportunity for flipping, then fear of missing out, especially for first time buyers, results in a stampede as people see the ladder going up and leverage themselves to get the last rung before it goes out of reach. But there was never any real scarcity in the first place.
Point being, a small amount of foreign investment can have a leveraged influence on local markets.
I do think the "foreign" word there gets too much attention though. The more important question to ask is - should property as an investment be something we economically encourage. How much economic activity does a $5M 3 bedroom house actually generate? I don't pretend to know the answer but I think this focus on the "foreign" bogeyman is blocking us from having more important conversations about the role of real-estate in economic policy.