If you have a look at post No. 188, the third picture (IMG_188.jepg), you can see three capacitors, two blue, one black. On the left of the blue 22uF/63V (seems to be c146) there is some soldering and a black SMD transistor. The cap seems to be bend away.
The tech may have been searching for the fault there (they often fix things to be sure it can be done cheaply, without a new, expensive board. Then they mess something simple up again, so the customer get's back a faulty unit if he doesn't pay for the repair).
In this case it looks as if he did a quick, not permanent fix just to check, as this is not going to last long.
You should get that fixed in a professional way. New cap and a new transistor or at least everything soldered clean and flat.
These amps and filters in active speakers do not last for ever, simply because of heat and vibration. Same electronics outside the speaker, in a well vented case, will have a much longer life.
Look for other areas of quick and dirty fixing, very carefull, with a lens and lots of light.
I did not understand what these polarity issues are, but that and a quick turn of a pot would make the speaker look defective, even if it was fixed, electronically. Look at the pot's, search for marks. I don't think the wanted to readjust the whole system, so I would simply mark the right position when I disadjusted it on purpose. Not that I do such things, but I know what tricks this trade uses were I live.
Changing only an A250 amp will take about 15 minutes, if you don't use an electric screwdriver. Serching for the fault on the filter board may take longer.
Anyway, if the know these speakers, they know the faults. ICE and ADAM products are very reliable in having typical, known faults. So they usually know what is blown in what case. Many repairs are not based on cost and time, but value of the object they repair.