All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We have not come across what you read, that it is not permissible to verbally say the intention (Niyyah) before reciting Takbeeratul-Ihraam (Takbeer for starting the prayer). Rather, this issue was subject to a difference of opinion among scholars; some held that it is recommended while others held that it is disliked. As for the case of Ghusl, it is sufficient for you to have the intention in your heart without verbally saying it, although saying it is not prohibited.
Shaykhul-Islam Ibn Taymiyyah said: “The Prophet, sallallaahu ‘alayhi wa sallam, did not say anything before reciting Takbeer. He did not pronounce the intention, neither in purification nor in prayer, fasting, Hajj, or other acts of worship, and neither did his Caliphs. He did not command anyone to pronounce the intention. This is the reason the issue of pronouncing the intention has been controversial among the later scholars. Some said that it is recommended along with the intention in the heart, as this is the view held by a group of the Hanafi, Shaafi‘i, and Hanbali scholars, justifying it as a confirmation of the intention and further fulfillment of it. Meanwhile, a group of Maaliki and Hanbali scholars as well as others deemed it disliked, and this is the opinion stated by Imam Ahmad and others; rather, they held that it is a disliked religious innovation. They explained: 'Had it been recommended, the Messenger of Allah, sallallaahu ‘alayhi wa sallam, would have done it or commanded the Muslims to do it. Indeed, he, sallallaahu ‘alayhi wa sallam, clarified all the deeds which bring one closer to Allah, especially the prayer, which should be learned only from the way he prayed. It is authentically reported that he, sallallaahu ‘alayhi wa sallam, said: 'Pray in the same manner you saw me pray.'
In brief, having the intention in the heart is indisputably essential. As for pronouncing the intention secretly, it is controversial among the later scholars as to whether it is disliked or recommended, whereas pronouncing the intention out loud is disliked, forbidden, and not from the Sharee‘ah, according to the agreement of Muslims.’” [End of quote, summarized from Al-Fataawa Al-Kubra]
Allah Knows best.