Can we always trust the PAPI lights?
Yes, you can trust the PAPI lights. As usual in aviation, safety is priority #1, this also applies to airport lighting, which is checked and monitored continuously.
PAPI lights are calibrated regularily to ensure their indications are correct. As with all technical equipment, there is a non-zero risk PAPI lights may fail, however, given how simple they are (literally just a light bulb, a colour filter and a lens - no moving parts) a failure is very unlikely.
You should note that not all PAPI lights are calibrated for a 3° glidepath. While 3° is most common, there are runways where the normal approach angle is different and the PAPI lights will be calibrated to that. So make sure to check the airport charts before using the PAPI system, or you may risk coming in steeper or shallower than you are used to.
Also note that, as pointed out by @wbeard52, approaching with the PAPI showing two whites and two reds is not a guarantee of obstacle clearance if you are far from the runway - it is only a guarentee that you are following the nominal glideslope of the approach procedure with which the PAPI is aligned.