I will try to explain.
If the phases are connected brown to U1, black to U2, and grey to U3 the motor will rotate in one direction swapping any two so for example brown to U1, Black to U3, and grey to U2 will reverse the direction.
We use a phase rotation meter which is a very slow revving motor so we can see which direction the phases are rotating.
However using the meter can land one with a problem as they seem to be rare items and often electricians don't check the sockets they install.
We had a problem with concrete placing booms in Sizewell 'B' Power Station and it can easy spread throughout a site. One cable was laid wrong way around so the at that time red, yellow, blue did not match and twisting the cores in a cable joint would not be small enough for the shells to fit. So the phases were reversed. This was not a problem to start with as next joint swapped them back. However it was shortened removing second joint.
Called out to a boom not working the electrician simply swapped the two phases but not at the WMDU but at the plug. Once moved again the next electrician selected a different plug or socket so the problem started to spread throughout the site.
By putting a plug on the phase rotation meter we were able to quickly survey the whole site and correct all extension leads and find problem WMDU and change the phases there too.
Pumps just don't work backwards but of course some plant can completely destroy it's self if run in reverse so very careful control is required. This is especially important when paralleling two generators.
Connecting Brown to Black, Black to Grey and Grey to Brown would still produce correct rotation so keeping phases correct colour is not same as getting rotation correct.
There are some areas of Liverpool which have the phases swapped even today after they were connected incorrectly during WWII and each firm swapped back at their premises so first one has to work out the normal and not jump in and set Brown, Black, and Grey as it may be wrong for area.
Since I do have a phase rotation meter I always test and if reversed I always advise the client of the fact.