They are placed by the branching order in which they are perceived to have evolved, or for creationist such as myself, in the order in which they were created.
Often the overall visual appearance is a poor indicator of heritage, one has to look at the finer parts of the flowers, sometimes with a microscope, to see some of the truly unique indicators that help place plants into their respective families and genera.
The dissimilarities which you mention, and the traits that seem to jump across the established heritage tree, lend addtional support to creationism, IMHO. :^)
- Tom

Taxonomy isn't really based on evolution but on shared physical characteristics. It is always changing. They decide something isn't quite right and rename it or move it. The goal is to have a descriptive name that is unique.

The categories get wider as you go up the "tree" so that plants in the same Genus are very similar while those in the same Family may not be as similar on face value as you would think.

Some plants that you would think are in the same families from their common names, are not. Calla lilies, canna lilies, daylilies, rain lilies, peace lilies etc. are all not in the genus Lilium though some are in the family Liliacea.

I could agree with everything you said except: "Taxonomy isn't really based on evolution..."

Could you give an example of where standard plant taxonomy follows physical characteristics, but not the perceived evolutionary/creationary heritage tree? :^)
- Tom

Linnaeus began by using sexual characteristics to group plants; later systems follow John Ray and use morphology in all stages of a plant's development to classify them.

A brief history of Linnaeus

Larry it's true that taxonomy will USE morphology (physical characteristics), but it is not the final goal and does not difinitively direct how plants are classified. Morphology is only one path to understand how plants are classified by their heritage(evolution or creation).
Take for instance my question above, it's important. There are zero examples where plants are correctly classified by physical characteristics but not by evolutionary/creationary heritage. In fact, when two plants seem related by an overwhelming majority of physical characteristics, but along comes one tiny invisible feature: DNA, which says true heritatge is different than it appears. Do the massive majority of physical characteristics win out? No, DNA & heritage do, and this has happened thousands of times in the last decade.
So, it would be 180 degrees wrong to say that "Taxonomy isn't really based on evolution...", since that is the real reason that morphology is even used by most taxonomers in the first place: to find & classify by what they percieve to be the order of evolution.
In fact even from the start, this quote from the link you provided describes Linnaeus' ideas on classification:
"The study of nature would reveal the Divine Order of God's creation, and it was the naturalist's task to construct a 'natural classification' that would reveal this Order in the universe".
- Tom :^)