It’s an attempt to make the limitation only that bad. They will only be guaranteed to differ by a constant if both languages are equivalent. If you choose between a Turing machine and a Turing machine with a halting oracle, the former will at best beat the latter by a constant, but the latter can beat the former infinitely.
You obviously can’t get it to work for all possible oracles, as there are uncountably infinite of them, but you can at least to it for all definable oracles, which is what this is.
It’s an attempt to make the limitation only that bad. They will only be guaranteed to differ by a constant if both languages are equivalent. If you choose between a Turing machine and a Turing machine with a halting oracle, the former will at best beat the latter by a constant, but the latter can beat the former infinitely.
You obviously can’t get it to work for all possible oracles, as there are uncountably infinite of them, but you can at least to it for all definable oracles, which is what this is.