Your logic is absolutely correct...I had a G3 800MHz, sold it to my brother-in-law, and several years later it developed the the GPU issue (I think there are multiple issues with the logic board). There was a "fix" in which you would place a shim between the GPU and the casing, which cause a little bulge, which would actually work...at least for a while. It died again later, for some related issues.
Note...opening up and playing around with the innards of a G3 iBook is *NOT* for the faint of heart.
I've had my fair share of run-ins with the G3 iBook (had a 14" 700 Mhz back in the day, and a used 12" 800 Mhz later on too), and IMO, the iBook was one of the worst laptops Apple ever released. If it wasn't the dreaded GPU BGA failure that got you, it was bad capacitors on the motherboard, or a voltage regulator module failure (a problem common with the early model G4 iBooks).
Shims, etc. will work but are only a short-term solution, as flexing from heat expansion/compression will lead to a worsening of the cracks in the solder between the GPU and the motherboard; I shimmed my 14" and it worked just long enough to rescue the data from the hard drive; I shimmed my 12" and it worked too, but I ended up having to use a C-Clamp to firmly press the computer against a tabletop to keep it useable. Eventually that failed too.
The next level would be to reflow the solder and resolidify the GPU connection to the motherboard. I really can't attest to the value of "Professional" Reball/Solder Reflowing Services; unless there's a reputable shop in your area, they can very expensive and even unreliable. There are all manner of DIY solutions (all accessible via Google), including tea lights souped up with alcohol, heat guns, and baking the motherboard in an oven (!). At this point you either risk (a) burning your house down, and/or (b) totally frying the motherboard. At this point, I'd say that it's not really worth it unless you really love your G3 iBook.
G3 iBooks are simply a bad investment, even if you're a tinkerer. Best to put that money towards a used MacBook, IMHO. I'd rather take a cheap MacBook with a broken screen over a perfectly working G3 iBook that's living on borrowed time.