They don't operate at arm's length from each other. President's Choice Bank, owned by Loblaws, has chosen to outsource all of their day-to-day banking and investment services known as PC Financial to the direct banking division of CIBC. Look closely at your PC Financial cheques next time. What's the institution number? It's "010", the same as CIBC. PC Financial and CIBC use the same call centres. PC Financial just has its own transit number(s) within CIBC but you're served by the same telephone service representatives. In really simple terms, PC Financial is but one branch of CIBC.
I think CIBC recognized that to retain their deposit business, they had to offer a really compelling Tax-Free Savings Account rate (their highest savings account pays less than 2.25%, with a $5000 minimum balance and all kinds of service charges). I think eventually they'll lower their TFSA rate to match the highest of the other banks (BMO, HSBC, Citizens Bank, PC Financial, etc.) but for now, to really get TFSA business and retain their own deposit business, they have to offer such a relatively high rate of interest.
Cheers,
Doug