That's the same tests they sell in my local poundshop - 3 tests in it for £1. I got my first, faint positive on those little sticks and bought a clearblue digital just to confirm, as that can be used up to 4 days before AF is due.
And do you know what - those poundshop sticks were showing that faint positive about 5 days early, going by my 9 week scan - so they must be good! But perhaps get yourself a clearblue digital as a back-up, if you're in any doubt.
As for the "false positives" - it's more a case that today's tests are so sensitive and can detect HcG so early on, even before your period would have been due, that very early miscarriages happen around the time women expected their period and are just like a period, so the woman sometimes assumes the test was wrong, not that she's actually having an early m/c.
The "danger" in testing positive (and knowing you are pregnant) so early these days, is that you will also be aware if you have an early m/c, which is upsetting. In the past, people were blissfully unaware and thought it was a normal period. This is perhaps what your neighbour is trying to warn you about: she probably isn't trying to "rain on your parade", she's maybe trying to stop you getting too excited (impossible though!) and then hurt if you have an early m/c.
M/C is what we all worry about in the first 13 weeks. It's such a fraught time, the early weeks, but also so exciting! Like the rest of us, you'll just have to impatiently count down the days till you get past 13 weeks.
Congratulations!!!
xx