I’m pretty sure the rental-only VHS copy I have uses the “plastered” logo too. I only remember that because it’s the same as on the original CAV laserdisc, and I remember thinking how that disc and the rental VHS seemed identical as far as the transfer went (whereas the original CLV is slightly different).
I’d normally double-check it to be sure but my primary VCR has been acting up lately. I do have a backup machine but it’s not currently connected. Maybe sometime later this week I can get that hooked up and confirm that for you… unless of course Rikter beats me to it.