That's a load of bullshit. What you describe existed for a brief period on NASDAQ Level II. It was never an edge in trading NYSE and AMEX stocks precisely because you had to send your order to the specialist.
If what you describe was fact, firms like Bright Trading that traded only specialist markets at the time would have been all over that strategy. I can still remember Bob getting irritated over the phone when I asked why his firm didn't offer trading in NASDAQ stocks. He said there was no edge because there was no specialist. He had just tried to sell me on their "trading with the specialist" opening orders strategy. I decided to go with Momentum. Fortunately it was not the Atlanta office. Not many will get the meaning of that reference. I had a laugh about a year or two later when I saw that BT began offering NASDAQ stocks.
Not to rag on the Bright brothers too much, but Don Bright used to come on here and say you couldn't make money trading index futures because futures led stocks and there was nothing that led futures. He challenged anyone to show up in their Las Vegas office to trade in front of him and prove him wrong.
Right before the pandemic, a buddy of mine who moonlights as a backgammon hustler got into an argument at a gathering about trading. The guy he was arguing with, who said he was a former prop trader, must have traded with BT because he said the same thing about index futures--they lead stocks but nothing leads futures so it's impossible to get an edge. He wanted to come over to my house and watch me trade so I could prove him wrong.
Rest in peace, Don.