I call bollocks.
A quick google tells me that it is possible to safely feed livestock (including cows) sugar beet. If it got them pissed I doubt these people would be suggesting it:
www.omafra.gov.on.ca/english/livestock/beef/facts/sugarbeets.htm
(Me, I'm not... in any way intoxicated, Thu 13 Oct 2011, 17:55, 2 replies)

Of course its bollocks
Sugar beet has been part of animal silage for centuries. You need yeast to ferment sugars, and yeast doesn't like living in acidic stomachs.
( ousgg is not seeking approval, Thu 13 Oct 2011, 19:46, closed)

But it works with the monkeys and elephants eating molasses...
...I saw it on TV when I was a kid. Giggled like a loon, so I did
(Professor Kenny Martin Hmm? What?, Fri 14 Oct 2011, 9:37, closed)

Apples have natural yeast...
one of those city-tv-chefs-living-in-the-countryside-and-fliming-it-for-telly jobs made cider from apples (duh) and they said that apple skin has on it/contains a wild type of yeast
(Darth Thump, Fri 14 Oct 2011, 12:16, closed)

Yes...
...if you mill and press your apples and leave them nice and quietly in a vat, that is what will happen.

But a cow's gastric juices are strongly acidic, and yeast won't work under those conditions.
( ousgg is not seeking approval, Mon 17 Oct 2011, 20:11, closed)

The key word in that link being 'processed'
Not raw - so not quite the same thing
(Godwin's Lawyer is more evil than Hitler, Fri 14 Oct 2011, 14:05, closed)

Buried in the page though is this:
"Cattle and sheep can consume unprocessed whole sugar beets."
It then goes on to explain who you may want to chop them up a bit to stop the animals choking.
I'm willing to believe that apples which have started to ferment may continue to do so whilst in a ruminant's stomach and, so, make them drunk.
Ruminants use bacteria in their stomachs to, for example, help break down cellulose into simpler sugars -- they don't make beer. This does not produce alcohol and bacteria which break down cellulose would not ferment sugar into alcohol.
[I only really googled this since the OP insists that nothing found on google disproves the theory. Simple common sense tells us this is extremely unlikely.]
(Me, I'm not... in any way intoxicated, Fri 14 Oct 2011, 14:30, closed)