That link is a water company - they run sewer systems. Your plumber is out of touch or you're using non-flushable wipes. The two types of wipes are not made the same.
Anything other than toilet paper, which is designed to disintegrate completely in water, should not be flushed. That includes facial tissue, paper towels, and cleansing wipes. If you have modern, smooth PVC waste pipes you might get away with it but the water treatment plant won't like it.
If you have older clay or cast iron waste pipes, feel free to take your chances as GP says. I'd rather not deal with overflows and I'd rather keep my money than give it to a plumber to snake out a clogged drain line.
Let's put it this way, are any of these "flushable" wipe companies willing to insure you against plumbing costs and damages caused by their wipes?
My plumber says that there are no wipes that are actually flushable, regardless of any claims made on the packaging.
We all know about advertisements and how companies lie to us. Why would this be any different?
I’m not taking any risks with our pipes, and we’re not flushing any wipes down the drain. Only human waste and toilet paper. Nothing else. That’s the recommendation from our plumber, and I’m sticking with it.
We’ve had our pipes clog up, and paid thousands of dollars. Fortunately for us, it wasn’t so-called flushable wipes.