I believe they do mean the fact that subtraction is just adding the negative and division is just multiplying by the inverse. You can look up field axioms to see how real arithmetic is really defined. It's much more convenient to have two operations instead of four.

The other commenter is correct, but another way to think or visualize is that any subtraction or division operation can be understood as an addition or multiplication.

X - 5 = X + (-5)

X / 5 = X * (1/5)

You can think of subtraction and division not being distinct or separated from addition and multiplication; instead, they're just a shortcut notation in mathematics because everyone was tired of having to write extra characters.

Figuratively, at least.

Addition asks "What do you get when you combine these two numbers?"

Subtraction asks "What do you need to combine with this number to get this result?"

Multiplication asks "What do you get if you add this number to itself this many times?"

Division asks "How many times do you need to add this number to itself to get this result?"

In many ways, all of these operations are syntactic flavor for addition. Subtraction is addition in reverse. Multiplication is repetitive addition. Division is repetitive addition in reverse. Exponents are recursive repetition of repetitive addition. And so on.

Look into the axiomatic proof of 1+1=2. It will shed some light on how mathematics is just complex notation for very, very simple concepts at scale.