Here's my best attempt to explain off the top of my head:

Ok, so imagine there was a hard fork proposed. For whatever reason, the fork seemed to be bad for your average user, but good for larger companies, including ones that issue stablecoins. The stablecoins, once they become widely used on bitcoin, (or any other chain) could end up being a decent chunk of the total value of that network. In the case of a hard fork, a stablecoin issuer (or group of stablecoin issuing companies) may announce they are only backing (honoring the right to redeem for USD) their fork of choice. They would obviously not be able to honor redemptions on both chains, as it would double the supply since their would be an identical copy of all coins or stablecoin tokens on both chains. At the end of the day, it's still every node runner's (user) choice on what chain to follow, but would they be okay with not siding with the people of the developing world by following the fork that would support the stablecoin that the poor rely on to use daily? What if the users running the node have some of their wealth in stablecoins? In addition, every added dollar of stablecoin value can be minted by depositing worthless fiat money, which enough could be printed, to be blockain-minted, to be a decent chunk of BTC's value easily, given that actual USD's marketcap is much larger in purchasing power than bitcoin's current sub $1trillion marketcap.

In conclusion, if a large amount of stablecoin value is on the network, it may cause users to make different choices than they would have normally, (in regards to the bitcoin network) to benefit a company (or cabal of companies.)

Hope I explained that right, I heard Odell explain it better on a RHR once.