I'm not sure that I'd agree. Although first of all, there are a couple options for how you turn the dish upside down, ie turning the whole mount upside down or keeping the mount the same, but turning the dish upside down on the mount. {I'm assuming this is an offset dish, since with a prime focus dish, there isn't really any difference between right side up and upside down, unless you have a spinclination mount.)
Anyway, if you turn the whole mount upside down, usually the elevation setting is set to give you your proper declination, given the BIG declination introduced by the bend in those motor shafts. For example, if you have a motor shaft with a 30 deg bend, and need a 6 degree declination, you set your dish elevation to 24. Now, if you turn the whole mount upside down, the motor axis bend still points 30 deg down, but now your dish elevation is 24 deg negative, giving you a total declination of -54 deg. There is no way to recover from this.
If you just turn the dish itself upside down, you'd be hit by the fact that the dish elevation is calibrated to compensate for the above mentioned offset angle, in the ~22 deg range, normally up. Like the other responder said, if you turn the dish upside down, now you have the dish aiming 22 deg down instead of 22 deg up, ie 44 deg in the wrong direction. The elevation adjustment may or may not be able to handle this, however there is sometimes the problem that when upside down the dish may bump into the mount/pole when turning, particularly when you'd have to dial in such a big elevation angle. ( I seem to remember this being an issue with one person I was communicating with once, although that may have been on a mount that didn't have an axis bend.).
Yes it can be done, and done right, but it isn't just a situation of turning the dish upside down and keeping the same settings. At a minimum, you'd have to dial in a significant elevation to compensate for the combination of offset angle/axis bend, etc, and in some cases this can require some modification.