That's not necessarily true. If they had the tank pumped, it would take awhile to re-fill and then the problem would be apparent. The tank itself is hardly ever the problem, usually its their drain field that fails. The house we sold a couple of years ago, some of our neighbors were on a "pump & haul" since their drain field had failed. One couple with small kids (lots of baths and laundry) had to have it done about every 6 months, so the OP not seeing a problem until after 3 months is not unusual.
To the OP:
You may want to check with your county/state health dept to see if they have some form of financial aid for failed systems.