Since ETH staking returns do represent a (sort of) risk free rate for ETH denominated loans, low fiat rates would pull down on those rewards, if the exchange rate volatility comes enough for people to stomach the currency risk.
The same sort of flows balance exchange rates and interest rates among national currencies, though as you point out, sufficient risks and controls abound to prevent complete parity between the rates.
I’d challenge the notion that one side is paying market rates, and one isn’t, at least in nominal terms. Bond purchases and ETH stakes are both market transactions at the prevailing rate, just with different structural forces in play.