Question: Do both Actaea and Fraxinus belong in the olive and lilac family?

Context articles: Fraxinus
Melia azedarach
Hardenbergia violacea
Spathius agrili
Rowan
Actaea (plant)
Actaea arizonica
Fraxinus excelsior
Actaea pachypoda
Syringa vulgaris

Fraxinus , English name ash, is a genus of flowering plants in the olive and lilac family, Oleaceae.
 It contains 45–65 species of usually medium to large trees, mostly deciduous though a few subtropical species are evergreen.
 The genus is widespread across much of Europe, Asia and North America.
Melia azedarach, commonly known by many names, including chinaberry tree, Pride of India, bead-tree, Cape lilac, syringa berrytree, Persian lilac, and Indian lilac, is a species of deciduous tree in the mahogany family, Meliaceae, that is native to Indomalaya and Australasia.
Hardenbergia violacea syn.
 "H. monophylla" is a species of flowering plant in the pea family Fabaceae, native to Australia from Queensland to Tasmania.
 It is known in Australia by the common names false sarsaparilla, purple coral pea, happy wanderer, native lilac and waraburra (which comes from the Kattang language).
 Elsewhere it is also called vine lilac or lilac vine.
Spathius agrili is a parasitic non-stinging wasp of family Braconidae which is native to North Asia.
 It is a parasitoid of the emerald ash borer ("Agrilus planipennis" Fairmaire, family Buprestidae), an invasive species which has destroyed tens of millions of ash trees in its introduced range in North America.
 As part of the campaign against the emerald ash borer (EAB), American scientists in conjunction with the Chinese Academy of Forestry searched since 2003 for its natural enemies in the wild leading to the discovery of several parasitoid wasps, including "Spathius agrili" which was discovered in Tianjin, China where it is a prevalent gregarious ectoparasitoid of EAB larvae in stands of "Fraxinus velutina", an ash species native to Mexico and southwestern U.S.A., and one ash tree endemic to the region, "Fraxinus mandshurica" and has been recorded to attack and kill up to 90 percent of EAB larvae.
The rowans or mountain-ashes are shrubs or trees in the genus "Sorbus" of the rose family Rosaceae.
 They are native throughout the cool temperate regions of the Northern Hemisphere, with the highest species diversity in the mountains of western China and the Himalaya, where numerous apomictic microspecies occur.
 The name "rowan" was originally applied to the species "Sorbus aucuparia" and is also used for other species in the "Sorbus" subgenus "Sorbus".
 Rowans are unrelated to the true ash trees, which belong to the genus "Fraxinus", family Oleaceae, though their leaves are superficially similar.
Actaea, commonly called baneberry, bugbane and cohosh, is a genus of flowering plants belonging to the family Ranunculaceae, native to subtropical, temperate and subartic regions of the Europe, Asia and North America.
Actaea arizonica is a species of flowering plant in the buttercup family known by the common name Arizona bugbane.
 It is endemic to Arizona in the United States, where it occurs in Coconino, Gila, and Yavapai Counties.
 Like some other species in genus "Actaea", this plant was formerly included in the genus "Cimicifuga".
Fraxinus excelsior — known as the ash, or European ash or common ash to distinguish it from other types of ash — is a flowering plant species in the olive family Oleaceae.
 It is native throughout mainland Europe east to the Caucasus and Alborz mountains.
 The northernmost location is in the Trondheimsfjord region of Norway.
 The species is widely cultivated and reportedly naturalised in New Zealand and in scattered locales in the United States and Canada.
Actaea pachypoda (doll's-eyes, white baneberry) is a species of flowering plant in the genus "Actaea", of the family Ranunculaceae.
Syringa vulgaris (lilac or common lilac) is a species of flowering plant in the olive family Oleaceae, native to the Balkan Peninsula, where it grows on rocky hills.
 This species is widely cultivated as an ornamental and has been naturalized in other parts of Europe (including the United Kingdom, France, Germany, and Italy), as well as much of North America.
 It is not regarded as an aggressive species, found in the wild in widely scattered sites, usually in the vicinity of past or present human habitations.