Connecting a 12v compressor with alligator clips?

I recently got a small 72l air compressor.

Mainly for topping up my tyres after deflating them for dirt roads and offroading.

After connecting the live, some guys suggest using an earth point on the chassis rather than the other terminal on the battery.

On the Jimny what other earth point can I use or is it OK to use the battery terminal?

All modern cars are negative earth.... hit Google up to see what this means

^^^^ Google should have informed you that the negative battery terminal is connected to the car bodywork, so in an electrical sense they are the same potential. All you need to find is an unpainted area that is connected to the body, a bolt head can be a good point etc.
So for the majority of older and modern vehicles it makes no difference if you connect to the body or the battery terminals.

Then things got complicated and clever.

I believe modern vehicles tend to have a shunt in the negative terminal, it's a device that lets the ECU measure the current being drawn from the battery. This allows for intelligent charging of the battery as the ECU knows how much energy to replace. It's not clear (to me) how much manufactures use this information, but if you connect your compressor directly to the battery terminals the ECU has no idea that energy has been consumed. If you connect to a body earth point and battery +ve the shunt is still in circuit, so it can see the energy used. This may not matter at all, but then it could, that's the bit that's difficult for me to define.
I know on BMW stop / start technology that the battery use is heavily monitored, you can't even swap the battery correctly without connecting software to tell the ECU it's been replaced.

If you have a GEN3 Jimny then none of this matters, it's nice and simple and has no clever tech, connect anywhere you want.

If you are not sure and want to play it safe connect between the body and battery +ve, keeping any potential shunt in circuit.

The general reason for not connecting to the battery is the risk of a spark which can blacken or pit your [soft] battery terminals. In an extreme case if the battery has been gassing (charged very hard) the spark could cause an explosion.

The advice probably comes from jump leads to start another car, then there can be a large current flow when connecting and a large spark. Connecting to the Earth point or chassis avoids damage to the battery terminals.

If your compressor has an on/off switch just make sure it is switched off, then connect wherever is convenient, it won’t make any difference. If it doesn’t have a switch the likely current will be small so it probably won’t make too much difference where you connect.