I don't know the source of this statement - is this a passage in the sutras? If so where?
(Thanks for adding the links to them in the question)
But I can answer from what I've heard in dharma teachings. Just in a basic way, some simple stuff.
So the thing is - yes you can end up clinging to rituals, and to practices. You can come to think that the whole point is to do those rituals.
But - it isn't the ritual that's the problem there. It's your attitude to them, and how you do them. There's nothing wrong with rituals, and they can be very good.
As an example, in the Tibeetan tradition, many Buddhists offer seven bowls of water to the Buddha every morning. It's a simple practice.
You put out the bowls of water. And the water symbolizes the traditional offerings made to a guest in India, so the idea is to invite Buddha into your life.
But you use water instead of the offerings of food, water, incense, flowers etc, because that makes it easy to do a simple practice where you don't get hung up on questions such as whether you have put out enough flowers to welcome a Buddha or whatever. Many people will put some flowers as well, and other things. But it's quite good to do the basic simple practice, just water, nothing else. The water symbolizes the offerings.
So then, as you do so you are welcoming Buddha into your life. Like - the compassion, the wisdom of Buddha. The path that he taught. But not as something purely external. As you do this, you recognize this as something you have in yourself. You then prostrate to the Buddha, and as you do so it's the same, prostrating to the awakeneed mind of the Buddha, recognizing it as something you have in yourself.
In this moment, you connect back to the historical Buddha, as if you were one of his disciples listening to him. It's as if, for a moment, there is no time separating you from the historical Buddha. Which relates also to the Mahayana idea that time and space in the strict linear way that we relate to them are also part of the confusion that binds us to Samsara and suffering.
So, that's a ritual. But what matters is not the ritual, but what it symbolizes and what you connect to. If you feel there is some connection with the awakened mind, and that somehow you are linking back to the teachings of the Buddha when you do this, then that's the whole essence of the ritual. The water really doesn't matter. Indeed having done it with water, you can also do it at other times ,just a prostration. No Buddha image, no water, just prostrating to the awakened mind, and making that connection to the path and recognizing it as something in you. You don't need the prostration either. It's something you can just connect to directly at any moment.
While, doing the ritual without that inner part to it, the essence of what it is about - well that does do some good. It's making a connection with the practice, which may later lead to you the inner meaning of it. But it's not what it is about really. If you were to then go over the top in some way and think the ritual is the essence of it - get really caught up in some details of how you do the ritual, get nervous about whether you have placed the bowls right, or filled them to the exact right level with water, or prostrated yourself at the correct distance from them or put them in the right position relative to the Buddha image or whatever - even with such a simple practice, you could make it hugely complicated. And that then would be this thing of getting too caught up in the rituals which this advice is warning you about. That sort of stuff really is of no significance at all. It's missing the point.
If you do the ritual and you get that connection, then you are doing it right. Doesn't matter if someone else comes along and says "you should stand three paces further away " or whatever. Who cares :). Do what they say if it makes them happier, but that's not what it is about.
Does that make sense?
You can also go over the top in any ritual. Or you can use them simply. And our life is full of rituals anyway. Things like shaking hands, nodding your head or whatever. It's using that to help connect to the teachings. The more that they connect to us in many different multidimensional ways the easier it is to fully relate to the Buddha's teachings in your life. And that's really what they are about. Little reminders that connect you to openness and compassion, day after day.
And some may not need them at all or hardly at all. Some might appreciate really elaborate ceremonies, you spend an hour or two hours a day chanting, visualizing things, prostrating or doing lots of other things. Some it's just a simple practice lasts a minute or two each day. A little meditation. Or setting out those seven bowls of water for the Buddha each day. Or whatever, we are all different, and things that work for one person may have little resonance at all with another. And that's just fine :).
With any practice you do the aim is to let go of the practice and connect somehow to the inner meaning, what it is all about. Even those who do long elaborate pujas with big intricate visualizations, hundreds of verses, sequences of mantras, mabye make big intricate mandalas. But the whole thing then is something you let go.
The sand mandalas of Tibetan Buddhism symbolize this way you let go of the rituals. They spend maybe a week building up an intricate sand mandala. Then they just wash it all away. That's the way you should relate to any rituals you do :).