Yes I've read that before and it's no surprise that Wednesday wanted their own ground when they were only taking a sixth of gate receipts at a home game. I don't think there is any doubt that Wednesday would like to have taken over Bramall Lane, being the best ground in Sheffield, but that wouldn't have ever been on the cards and operating as a professional club renting the ground for every home game wouldn't have been satisfactory.
Nevertheless, that hasn't anything to do with the general belief that Wednesday moving to a new ground left Bramall Lane so short of revenue that it formed its own club. FA cup games were the biggest at the time I believe and in the 4 years before they got their own ground, they played 4 home games in the cup, presumably at BL. The two years before United were formed they were at Olive Grove. So where is this massive shortfall of cash? How many other games did Wednesday play at the Lane that would have brought high gate receipts? Before 1880 they would have played lesser games elsewhere. Local mini-cups and friendly matches would surely not have brought that many through the gate, or maybe I'm wrong, but I can't find any information about other games played in those years.
There were lots of other teams around at the time, some as big as Wednesday I think, like Heeley. DId they play at the Lane occasionally?
I just can't see how Wednesday were providing Bramall Lane with a decent revenue stream leading up to our formation. We know they weren't in the two years prior, so I really don't think "loss of gate receipts" was a factor in our formation - rather a vision of a future which involved high gate receipts from regular football played by a professional team, something that Sheffield hadn't seen up to that point.