The industry sponsored project program from BCIT (from which I've hired students before) is a way to use student software developers to being to solve a problem you have. If the BCIT international office has received instructions from IRCC that this is considered work - and since it revolves around delivering a software solution to a sponsoring company, it may well be, even if you're not compensated for it - then you need to listen to your International Office.
If it turns out that IRCC believes that this part of your studies is work and you needed a co-op permit for it, and they seek enforcement against you for violating the terms of your permit, you could be looking at deportation and bans from Canada.
Yes, I know that other students didn't get the permit. But instructions change, programs change, and IRCC's opinions of things change. There is a reason why your International Office sent the paperwork around. Check with them. If they're wrong about this ISP, then maybe you don't need the permit. But maybe they were wrong before now. Or maybe IRCC's opinion of the project has changed.
Since you have time to apply for the permit, you do not want to risk going without it, in my opinion. Unless you talk to the BCIT ISO and they say "Oh wait, for ISP you don't need a permit. Our mistake. Sorry."