There is also a significant possibility that what this plumber told you is complete crap. IF the situation is as he says, then the result is POSSIBLE.
The key to me is the extensive work that he says is necessary. Here is how some contractors work. (1) Figure out what kind of replumbing job you would like to do; (2) Fit the "diagnosis" to the job.
What you MIGHT have is a simple blockage.
I would call AT LEAST one other plumber, preferably one with a stellar reputation for integrity, like Terry and HJ and CacherChick and other of our members have. Angie's List, BBB, other sources can give you an idea of who is competent and honest. Everyone will always have a couple of bad reviews: read them and see if it sounds like a person with knowledge wrote them, or it's just some idiot who never understood what the issue was and is mad because the problem cost money to fix, or vindictive drivel or worse a competitor. Compare that to the positive reviews. Is this a guy who came in after Roto Rooter told the customer that the lawn needed to be dug up and used a proper snake and got the line clean and thoroughly-opened for 1/20th the cost? Is this a guy who did a $100 simple repair that worked properly a year later when the other guys wanted a $1500 solution? And check out the guy who wanted to excavate your basement, too. What are his reviews?
The plumbers I use (Maccarone in Long Island, NY) are comparatively-expensive, no doubt about it. They also come promptly, diagnose the problem correctly, use quality materials, and do the job right the first time. They also never propose to sell me anything that I don't need. Usually quite the opposite. So I pay a lot for what they actually are doing, but I save a lot because the repair is good for eternity and I don't end up paying a "bargain" price for work that was never necessary in the first place.
A recent Maccarone anecdote. Friend has leak above ceiling in important room of very expensive home, ruining big section of plaster ceiling. Thinks it's the toilet on the floor above. Maccarone comes out the afternoon I call them. They look at the ceiling, decide it's a two-man job, and reschedule for next work day. They show up on time, properly-prepare the fragile decorated room in which they are working, then cut a hole in the ceiling. As they are doing so, they notice that when you look at the ceiling in a particular way, you can just make out that the same area has been repainted. Huh. Floor above was only added about 8 years ago and this whole ceiling doubtless repainted then. Strange. Once up in the ceiling, they get off the ladder without touching anything and tell me to climb up and look at what's there. It's not the toilet; it's obviously the drain piping from the tub/shower. And though pretty-new construction, it has very plainly been repaired once. Poorly. Wrong fittings, wrong pipe diameters, etc., but those don't cause a leak, they just indicate questionable workmanship. We run a test with a bucket under the section. Yep. Water comes streaming out. Leaks were from multiple places in the repaired section. One obvious problem was that when you pulled on the section of the pipe leading to the trap, it slid right out of the fitting to which it was connected. Improperly-"glued". Same thing in a couple of other places. Amazing. So they cut the repair work all out and redid it correctly. We ran a couple showers worth of water through; no leaks. Left the ceiling open to test it again later. I would never post photos of the friend's place, but you can tell by looking at the job (at least I can) that the workmanship was night and day.
So the lesson of that experience was this. The whole thing took a few hours and cost a good deal of money. But how much did the previous homeowner save by calling out the guys he did to do the poor repair? Twenty percent? Thirty percent? Meaning two-fifty? Three-fifty? Anything? So now coming out to redo the crappy work costs several times that, and probably similar for repairing and repainting the ceiling so that it looks like it never happened. Perhaps the prior homeowner wasn't even trying to get a reasonably-priced job. Maybe he just called the wrong people -- how would he know?
Remember that the smoothest, nicest, most-seemingly-concerned contractors are often the biggest snakes. Don't mistake kindness for competency or integrity.
You wouldn't have a heart transplant without a second opinion. Don't get a plumbing transplant without one.