Burke's is sufficiently condemned by not citing sources. But they can certainly be charged with knowingly printing wrong stuff.
In the 19th century, their main method of "research" was writing to heads of families. They got the official version. In the Landed Gentry books, the less important people paid for their entries.
Everybody knew that many of the pedigrees were fakes. The people who bought the books were the people in the books, and they knew they'd had work done on their own story.
And in effect Burke's offered an update service, so Sir George could let it be known that as of the 17th edition he was a distant cousin of the Marquess of Exeter, but was not and never had been a kinsman of the Duke of Yorkshire (such a shame about his sister).
This of course was what people needed to know. They could get the dirt on the grapevine, but heaven forbid that people should print that sort of stuff, society would fall apart.
So Burke's became the gentry's official history of themselves. Nobody then thought that genealogy ought to be about true history, and there wasn't any money in that.
The publishers oiled the wheels by adding those misleading preambles which imply that Sir George was descended from Sir John who did homage in 1197 and Lord Richard who fought so bravely at Agincourt, although there wasn't really any connection.
However, they've always been very slow to follow up on actual research, and continue to print debunked lines long after they're debunked, until they think the market favours dropping them.
And the current publishers, still intent on giving the customers what they want, now seem to be cynically picking up discredited immigrant lines from 19th century American books.