I'll consider specifically the GPLv3, since to my mind the terms in it are more tightly defined, and since you don't ask about any particular, older version. I'll also consider only software in which some third party has a copyright interest, which interest they licensed to the ISP under GPLv3; the analysis is different if the ISP is the sole rightsholder in the affected software.
The obligations are placed on the your ISP by the act of conveying binary software covered by GPLv3, by s6 "You may convey a covered work in object code form under the terms of sections 4 and 5". Both s4 (which applies to verbatim copies) and s5 (which applies to modified copies) require that the software be conveyed under GPLv3 (ss4, 5c), and s6 obliges them to provide source code (plus build scripts, makefiles, etc., as per s1).
What is conveyance? From s0,
To “convey” a work means any kind of propagation that enables other parties to make or receive copies
Well, you've received a copy, in the device you currently hold. Did the act of providing it constitute propagation? s0 also says that
To “propagate” a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification)...
That says nothing about transfer of ownership; the ISP merely has to make, and/or to provide you with, a copy of software that they would have had no permission to copy and/or distribute had the GPL not granted it to them. Subject to the stipulations at the top of my answer, this they have done. So it seems to me that the executable copy of the GPL software (if any) in the set-top box you hold has been conveyed to you by your ISP. Their decision not to sell but to rent you the box containing it doesn't change this.