Though I must admit that it's doubtful for them to find enough cash to take the other side of this bet, so most likely they have to resort to actual Bitcoin bought from liquid exchanges or OTC.
They absolutely can find counterparties to take that trade, but it would be much more efficient to trade in the spot markets. The real question is if they have custody operations setup to handle the coin.
I expect they outsource these backend operations to the likes of Coinbase, Gemini, or Fidelity. They probably won't allow customers to transfer their Bitcoin out until they move custody in house, which is no easy task.
As long as an entity (such as the government) prints money and takes the hit on the spread people will see contracts of BTC as equivalent as BTC w.r.t value. Its basically banking, but since fiat is still the prime currency of legal settlement (not BTC) no one will think its possible to "run the bank" as that entity in the event of a run will pay the difference. BTC is not actually required to settle anything by most countries laws, so actually delivery of BTC isn't guaranteed. This does undermine actual BTC especially if actual BTC is harder to spend - the pseduo-BTC would then have more utility.
In other words BTC could be the same as fiat potentially in the longer term. It will be more transparent of course since it it easier to take delivery of than say gold (or cash but less so), but as long as they don't give you that option in your product that's fine. Even cash is like this with withdrawal limits, and other laws. If fiat was only valued by the actual cash in the economy it would be worth a lot more than it is now btw.
Why? If they never offer withdrawals then they don't need to worry about that.
This is the same idea as bucket shop operations that "trade" stocks with their clients without actually processing trades on any exchange.
When prices are rising, with new buyers available, then a bucket shop can do just fine for themselves. As soon as they have more sellers than buyers, at a price higher than they came in, the shop is the one that has to cover the difference.
Admittedly this doesn't sound right to me, but it's what the parent commenters seem to be saying.
As Matt Levine pointed out yesterday, a mainstream company can make money by buying Bitcoin and then making an announcement that sounds like they're going to use it. (It doesn't matter whether that plan works out or not, as long as the price of Bitcoin goes up.)
For Paypal, getting their own customers to buy Bitcoin (that they already own) would be a way of hedging, if they're long Bitcoin to begin with.