We should be saying olive rather than apple

pic from https://commons.wikimedia.org/wiki/File:Centenarian_olive_tree_1_(4752183682).jpg

That is we should be saying "the olive doesn't fall far from the tree." That would reflect the halacha that says you can identify which tree an olive is from. The same does not hold true for apples or other fruit.  In the case of most fruit you'd find in the road, you can assume hefker status because it is considered impossible to determine which tree bore the fruit. In contrast, an olive can be identified as coming from a specific tree.

Rav Goldwicht stated this in a special Tu B'Shvat shiur he delivered this Sunday in NYC on the occasion of the yahrzeit of Rabbi Copperman (see http://kallahmagazine.blogspot.jp/2016/01/the-life-of-rabbi-copperman.html). He connected that halacha to the blessing for a household expressed in Tehillim 128:3

Your wife will be as a fruitful vine in the innermost parts of your house; your children will be like olive shoots around your table.

גאֶשְׁתְּךָ | כְּגֶפֶן פֹּרִיָּה בְּיַרְכְּתֵי בֵיתֶךָ בָּנֶיךָ כִּשְׁתִלֵי זֵיתִים סָבִיב לְשֻׁלְחָנֶךָ:

Rav Goldwicht raised the question, what's the blessing in having children comparable to the growth of olives? The answer is to be found in the halacha, The olive attests to its tree. So too, the blessing for a good person is that his offspring will be like him.

The same theme of the blessed tree source is what we find in Taanit 5b

When they were taking leave of one another, Rav Naḥman said to Rabbi Yitzḥak: Master, give me a blessing. Rabbi Yitzḥak said to him: I will tell you a parable. To what is this matter comparable? It is comparable to one who was walking through a desert and who was hungry, tired, and thirsty. And he found a tree whose fruits were sweet and whose shade was pleasant, and a stream of water flowed beneath it. He ate from the fruits of the tree, drank from the water in the stream, and sat in the shade of the tree.
And when he wished to leave, he said: Tree, tree, with what shall I bless you? If I say to you that your fruits should be sweet, your fruits are already sweet; if I say that your shade should be pleasant, your shade is already pleasant; if I say that a stream of water should flow beneath you, a stream of water already flows beneath you. Rather, I will bless you as follows: May it be G-d’s will that all saplings which they plant from you become like you. So it is with you. With what shall I bless you? If I bless you with Torah, you already have Torah; if I bless you with wealth, you already have wealth; if I bless you with children, you already have children. Rather, may it be G-d’s will that your offspring be like you.