Just providing my "data point".
After not applying for anything since 2009 (added as AU on spouse's Freedom March '15, April '15 FICO ~770), I was auto-approved for Amex Plat (personal) and CSP ($21k) on April 8th. I applied for Amex SPG (personal), Chase Freedom, and Chase Ink Plus on the evening of June 14th. SPG (5k) & Freedom (3.5k) were auto approved, but Ink Plus was "received".
After some preliminary reading, I called recon the next morning and was told I was denied for Ink Plus due to two applications in a single day. After advocating my position, I was denied for too new of a business (landlord since '12) / too low business revenue ($2X,XXX). I called back late that night and advocated in greater depth and was told after 30 minutes of back-and-forth that I was recommended for approval for 5k. I finally received email confirmation of Ink Plus approval (5K) on June 18th.
Based on additional reading, I strongly believe that I would have been approved after a few days had I not called recon. Nonetheless, it all worked out for me. I hope this helps someone.