I wouldn't say no basis... but yeah, it's really quite phenomenally wrong.

Well, I'm told that "Islam" translates roughly to "submission", and most of the common theophoric names in the Islamic world include an "'abd-" (or "'amah-", for female names) component, meaning servant or slave [of God]. It's not clear to me how much this is supposed to imply literal slavery as opposed to running with the standard temporal hierarchy metaphor you find in most monotheistic religions, but it's suggestive, at least.

References to slavery seem rarer in Christianity, but it does use a lot of verbiage suggestive of royalty or nobility, and most of its early evolution took place in times and places where slavery and subserviance (rather than mere loyalty) to a lord were easily within spitting distance of each other.

On the gripping hand, this is all supposed to be based on willing subordination to God. "Forced into service" doesn't seem to describe the psychology very well, from where I'm standing.