Those guys are right. That place sounds like one of those golden scams. Flight schools are famous for them. They make it sound like a great gig, but it's far from the truth.
If you want to get done as fast as possible, take their advice and go to www.allatps.com; spend $40,000 and then flight instruct for a while to build multi time.
You can get hired by a regional airline with around 500TT and 100 multi these days and they will give you your ATP certificate for free when you're ready to upgrade. You'll still probably save $20,000 and at least one year off of that program you found.