Especially if the main thing keeping a lot of people out of the market is raising a down payment, not affording the monthly mortgage. To make a down payment, you "only" need a few 100k, not millions. It's in reach for people receiving significant equity value from their employers along with strong salaries, you don't need to get boosted into the ultra-rich.
1) A lot of new employees who make 1-2 millions (maybe not rich, but 'some money') means more demand on housing prices.
2) It does not take a lot to keep the bubble going. Less than 2% of the buyers, if they are 'price inelastic' (i.e. they'll pay whatever the asking price is) is enough to keep a bubble going. This happened in Vancouver - as soon as foreign buyers paused due to new taxes, prices fluxed quickly. They don't represent a large chunk of the buyers.
If 95% of them are looking around, and 5% are just buying 'at whatever price' - those people will drive pricing.
When 'the house down the street' sells for 10% above asking, it validates all the homes sales in that environment, and gives confidence to the regular buyers that their investment is sound.
If there is ever a hint of a plateau, all it takes is for a few price-inelastic buyers to come along and 'validate' prices. Then some buy on that basis, and the pricing cue percolates through the system.
Once those people leave the market - there's no strong validation going on - and a small whiff of lack of price movement can put a chill on things, then prices can start to fall.
Once they start to fall - it's a negative signal, wallets clam up. Without a rich buyer to restore confidence ... the spiral continues.
It'd be an interesting model :)
If you want to see when those price inelastic momentum makers have left the market, watch the trailing 10, 30 day listing to sales price ratio. 10 day trailing gives you a hint, but it should be clear as day after 30 days when you see inventory selling consistently below asking.
The claim was that 'foreign buyers' were not driving up prices, but clearly they were.
And the tax didn't even imply that all foreign purchases dried up, just that some would have, and the price-point of their purchase decision would have changed somewhat.