There is at least some evidence that this is true. But why?:
The researchers suspect the difference may be driven by genetic changes that accumulate in the actively-dividing cells in the tip of the plant shoot as it grows. Cells don’t copy their DNA perfectly each time they divide. In animals, most DNA copy mistakes that occur in the cells of the animal’s body can’t be inherited — they’re evolutionary dead ends. But this isn’t the case for plants, where genetic changes in any part of the plant could potentially get passed on if those cells eventually form flowers or other reproductive organs
Hmmm. From the wayback machine, when gene mapping first attracted attention a decade ago:
Gilbert introduces his lectures on gene sequencing by pulling a compact disk from his pocket and announcing to his audience, “This is you.”*
No. It ain’t.
It probably ain’t even a weed.
Plants by nature grow toward a suitable light source. Most plants that remain short by growth habit are likely responding to other factors. In northern regions, reducing heat loss is critical. Virtually all Arctic plants are comparatively short** because getting rid of most of the stem reduces heat loss. Some short plants in dry areas conserve water by reducing leaves or even developing a spherical shape.
What we don’t know is how readily plants will just change their habits in response to different environments and what genetic mechanisms enable them to do so.
*(Dorothy Nelkin, “Less Selfish than Sacred? Genes and the Religious Impulse in Evolutionary Psychology,” in Hilary Rose and Steven Rose, eds., Alas, Poor Darwin: Arguments Against Evolutionary Psychology (London: Random House, Vintage, 2001), p. 18. )
** A century ago and more, schoolteachers in the North American Arctic had to try to explain what a “tree” is to people who had never seen one or imagined its possibility. The situation also posed a challenge for Bible translation. (For fun, if you read or hear the Bible read, consider how you would respond if you had no idea what “tree” means. = A plant that can be taller than a human? Really? Even though it has no internal heat source? Aw come on!)