Actually this is not true. Applying for the older (no longer available) Schwab Invest First Visa 2% cash back card, one of my bureaus was frozen and a lady called and informed me that they were going to pull from another one because of that. They were able to recognize the freeze and work around it. I had left one bureau "unfrozen" since they did not offer an on-line freeze. They now do. Of course, not all issuers will be this thorough.