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If I'm not mistaken that BofA link posted only checks to see if they have any currently standing offers for you in their database. It doesn't actually soft pull your reports. So pretty much it checks to see if BofA has recently PRM-inquiried you to send you any pre-approval propganda. I think the AMEX is the same way as I have yet to see any softs left behind on any of my reports. The HSBC does indeed soft your EQ report.
I got pre-approved for the bbrz platinum, tempted to apply for it but decided I didn't need another rewards card so went for the BB Store Card and to my surprise I was approved for $2500 CL on the Program B tier. I have applied for that card twice and have been declined but that was last year and i have gotten more credit history since then.
"Pre-Approval" is simply marketing hype. Don't get sucked in. Be proactive rather than reactive. Apply for cards which make sense for you.............
anyone have a link for the store card