He said miners will mine more at the same expense, not just "more." That is true if difficulty were to drop. Individual miners will use the same electricity to produce more coins for the same cost in power.
Miners will not "mine more at the same expense". They will mine the same thing at less expense.
Individual miners cannot "produce more coins for the same cost of power" if not other miners "produce less coins for much less power".
Because the total number of coins mined must be the same.
If some use "the same amount of power" and hence "mine more", then that means that other miners mine less, and consume vastly less power (maybe stop mining all together).
Globally speaking, the miners mine the same amount of coins, and use less electricity. The do not mine more coins with the same consumption. Some do, and others mine less.
That means that miners make more profits (or lose less money, depending where they come from).
The point is that it could be that those increased profits go into hodling coins. That's the ONLY way in which difficulty can have an influence on the price: by increasing the demand for holding coins (by the miners themselves, because they want to allocate their profit in coins).
If difficulty goes down then a miner will mine more coins with the same machine. The same machine will obviously continue to use the same amount of power. Not sure where you are getting your information but it is inaccurate.