I don't believe so. It is indeed just an early fade.
I'm not sure it's just a fade issue. My memory is that the 45 is a different mix as well.
I've got the 45 version logged as being correct on A Kick Up The Eighties Vol 8.
Edit. I may be getting mixed up here. It might be We Are Detective that's the different mix? But I have a list of 9 Thompson Twins singles with specific CDs identified for the correct length and/or mix.
Thompson Twins - Love On Your Side (The Greatest Hits Camden)
Thompson Twins - We Are Detective (The Greatest Hits Camden)
Thompson Twins - Hold Me Now (Platinum And Gold)
Thompson Twins - Doctor! Doctor! (CD single)
Thompson Twins - You Take Me Up (Kick Up The Eighties Vol. 8)
Thompson Twins - Sisters Of Mercy (Platinum And Gold)
Thompson Twins - Lay Your Hands On Me (Platinum And Gold)
Thompson Twins - Don’t Mess With Doctor Dream (The Greatest Hits Camden)
Thompson Twins - King For A Day (Platinum And Gold)
Also Watching I don't believe is on CD in its 45 version.