I reckon any teacher that tells their pupils this should be instantly struck off, for not knowing what they're talking about.
This is a thread that repeats itself every few weeks on here- and there will be employers who will employ Oxbridge grads on the basis of the name on their degree. The employment statistics don't tend to support the idea that its worth an extra degree banding though, just that Oxbridge have a top record in employment prospects. You could probably search on first from ex-poly vs 2:2 from Oxbridge to see this debated numerous times on here, so starting it again probably isn't necessary.
What I will say is, some universities, particularly newer ones, give out lots of firsts- perhaps in an attempt to boost their ranking. Much of the Russell Group have typically less than 1/7th of students receiving top marks (in arts even less), compared with up to a third at some other places. This might well be devaluing a degree- making people think lower degrees from better unis are worth more, but the blame for this must lie with those who were prepared to indulge in degree inflation in the first place. Its bloody hard at some of the ancient universities to even get a 2:1 (and, since league tables rank on things like % of firsts/2:1s and dropout rates, you can end up lower down merely by keeping standards high), whereas thats not always the case across the board.