The Smith Institute report says:
"As overseas buyers seek out homes for investment purposes they risk pushing prices up and reducing the availability of homes to buy for local people."
It does not "RISK pushing up prices" it DOES push up prices, in exactly the same way as Buy-To-Let investment has inflated the UK housing market significantly.
For decades now we have had the absurd situation that private investment in housing receives significant tax advantages, by giving income tax relief on property purchases made as part of a "pension investment portfolio" (typically 40%) and by making the profits gained when the asset is liquidated exempt from capital gains tax.
This has turned housing into a profit-making machine that gets more effective the more supply is restricted. This is not good for society and it is not good for the economy either, because it takes private investment funds away from more conventional investment media such as stocks and shares that help to support UK industry.