While you haven't said anything WRONG, that's only a small part of the issue. If you're talking REGULATED wall wart at 6V and battery charging is NOT involved, you are pretty safe using anything over the minimum required.
But most wall warts are NOT REGULATED. And the worst of the bunch are the switchable voltage ones. The voltage printed on the label is a nominal guideline voltage at some unspecified load conditions. Two different brands with the same numbers on the label can have significantly different voltage output at the same current. The voltage can be much higher at low load. So if your adapter is rated for higher current, your nominal load will be a smaller percentage of rated and the voltage is likely to be higher...sometimes a LOT higher. Especially when you turn the device off, the voltage may increase enough to damage some internal parts ahead of the switch.
Then there's the size of the barrel connector. If it's just a little too big, it can spring the contact so the thing won't run on batteries any more. It's fun to go to Radio Shack and watch the "we got answers guy" try to cram different sized connectors into the customer unit.
Your problems multiply if the adapter charges internal batteries. Battery charging is often carefully tuned to the AC adapter characteristics to save that last penny. An adapter that's too powerful can severely unbalance that equation leading to smoke.
Call me paranoid, but weigh the cost of the TV against what you'll save by not buying the vendor recommended adapter. Is the difference worth the risk. Even if it works 99% of the time, somebody has to be the 1%.
Now, if you've got the instrumentation and are willing to test the process over the range of conditions, you can make almost anything work. mike