I do not know where you are from but if the flushable wet wipe, that is called "wet toilet paper"(translated) here, almost completely falls apart without the support of a sheet of normal tp, I am pretty sure that it's okay to flush it. Feel free to check out this product page.
Edit: The link seems to be down now. No idea why. There are a lot of other examples, though. Here's the archived link.
I need flushable and non-flushable wet wipes on this.
Edit: I did not know that in some parts of the world "flushable wet wipes" and "wet toilet paper" are not synonymous and learned that e.g. the USA has a problem with companies being allowed to advertise their wet wipes as "flushable" not because it is okay to flush them but because one is able to.
Reminds me of the time uncle Rob told me how to wrestle properly.
The trick is to not wear any clothes to keep them clean from the special wrestling oil he gave me, so mom doesn't have to wash them.
I'd let seven oj's fight seven glasses of milk in my stomach, down the strongest coffee known to humankind afterwards and then wonder why my tummy hurts...
In case anyone is interested in reading the text on the right: