This Sanskrit verse is from Puranas and is intended to mean differently than what is translated literally above. To understand the full import of this verse, we need to understand the purpose and place of the Puranas in Hindu tradition.
Puranas constitute Hindu mythology. Hindu mythology is not written to provide emotional or intellectual entertainment, or satisfy one's idle curiosity. The sole purpose of the Puranas is to bring forth morals to help build one's character. Thus, Hindu mythology is moral-based. This means that each episode is designed to bring forth a particular moral (or morals) for the development of one's conduct in one's individual, social and religious life.
Although Puranas are called secondary scriptures, they are not scriptures in the narrow sense scriptures are understood in other religions. Puranas are tales and fables, which were created in the ancient times to expound teachings of the primary scriptures (called Sruti) for the benefit of those, who could not comprehend the deep philosophy of the primary scriptures. Some of the Puranas are based upon true-life stories of the ancient kings, queens, and heroes. Others are based upon only imagery and imagination. In Puranas, neither genuineness of the character is important, nor is the purity and truthfulness of the story. Only the moral is important. This is why there are some popular religious stories (such as Satyanarayan Katha), where even gods are depicted as mean, power-hungry and revengeful, and in some cases outright mean and partial. However, when you look at the moral of the story, it is meaningful and wonderful. Whether the story is true or not is immaterial.
Sexual energy is the most potent energy in humans and animals. In animals, it is controlled by the Nature through a control system called instinct. In humans, it is controlled by the free will exerted by the mind in three different ways. By self-control (celibacy), this energy is transformed into spiritual energy, as has been demonstrated by Yogis of India over thousands of years. In addition to attaining spiritual perfection, these Yogis were able to develop supernatural powers by transformation of this energy. Through the institution of marriage, this energy is transformed for constructive purposes, such as raising one's family. If uncontrolled, sexual instinct can lead to one's own physical and spiritual degeneration. In Hindu tradition, a gown-up unmarried daughter is advised to keep a distance from her own male relatives and friends. Even the father is advised not to spend time alone even with his own unmarried grown-up daughter, lest the impulse may overtake his judgment. In Hindu culture, at least in ancient times, many restrictions were placed on women for this very reason. With this background, let us analyze the above verse.
"On seeing his beautiful daughter Padma, Brahma was sexually excited. He wooed his daughter and wanted to copulate with her."
Here the story is not viewed to be real, only the moral is to be considered important. The moral of this story is that a gown-up unmarried girl should not be allowed to remain alone in the company of a male. This guidance even applies to the father of that girl. This is why, in Hindu culture, even a father is advised not to spend time alone with his own grown-up unmarried daughter. This is the message the ancients wanted to bring forth for their society through the above verse.
"How could a daughter give consent to her own father? Padma refused. Brahma could not give up his desire. He began to quote the Vedas to convince her that there was nothing wrong in having sex with anyone, anytime, anywhere for the sake of giving birth to a child."
This simply means that the sexual instinct is powerful (it does not matter, whether it is a Hindu or anyone else) and a man will try to give all plausible arguments to seduce the woman (even try to interpret scriptures to help satisfy his lust). No Hindu scripture allows free sex in order to give birth to a child. Sexual energy must be controlled through the institution of marriage to create a family in accordance with the demands of Dharma (Hindu moral and ethical code).
In conclusion, the above verse (and entire Hindu mythology) must be studied with questioning attitude. Why should such a verse appear in a scripture? What is the purpose of such a description? Once such questions are raised, the answers are intuitive.
I reviewed the contents of the web site:
http://www.periyar.org/mr/984mr12.htm
It appears to me that the intent of the sponsors is to literally translate Sanskrit words into English and make their conclusions based upon their own understanding (rather misunderstanding). A conditioned mind cannot see with clarity, because its own conditioning clouds its vision.