By the way that's worded, it sounds like a case of sensitivity rather than the method. If you change one of the variables to a unit that is way out of scale, then it's quite possible that the results of PCA, and many other methods, will change. But that's because it's not scale invariant, and so if you want good results you need to present your variables in the same units, and/or in some normalized format (zscored, etc.) where the scale of one unit doesn't blow the others out of the water.
These methods are not magical, and they are not intelligent. They do not know what they're looking at, so it's your job to feed them something reasonable.
That said, if you take some physically grounded data and change units, you won't recover different eigenvectors as long as your input data is good. The physics doesn't care about the units, or the coordinate system, or whether you use python or anything else.