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Opening any type of account at a bank or CU will get you a hard pull.
When I took advantage of the free $125 early last year it was only a soft pull. I already had a CC with Chase though. It might be different now. I would not take the word of anyone inside the bank either. Not too many know what they are talking about unfortunately.
That's been our experience as well.
But, we did not experience any FICO score drops for those hits (or for most others, for that matter).
Because the checking account doesn't report on your CR, they, of course, aren't included as a new account, and don't hit your AAofA - both of those issues are more likely to affect your FICO scores. Hard pulls are not so damaging - really. It's just a minor shock to your system if you're not expecting it.
I opened a Chase checking and savings account online and they didn't pull a hard one on me. They pulled a soft and 2 hours later I got a welcome email and 5 days later got my checks and debit card. And I don't even have a credit card with them. Weird
can't say i recall, actually....it does seem to be the common thing now.