Are Subaru's just as reliable as Toyota's & Honda's? Or is that just a rumor?

Sources or your own personal experience would be nice, thanks.

Subaru engines will last forever if properly maintained. Their older cars, back to the 70's and early 80's had a few problems, but their newer cars are much improved and I would think they are every bit as good as a similar Honda or Toyota. PLUS, Subarus come with all-wheel drive as standard equipment.

Subaru's are almost as reliable except they leak oil and antifreeze at the head gaskets. It does not affect it as in coolant into oil. It leaks external and if you keep it topped up you will be fine besides that they are a reliable car

Reliability varies based on how well you maintain a car but yes, Subaru is as reliable as Toyota and Honda for most models. I would avoid the Tribeca and the BRZ if you are worried about reliability, but everything else is solid.
The head gasket issues Autotech is referencing is not applicable to Subaru's made in the past 5 years. They resolved those issues. If you are buying used before the 2009 model year, then his advice is sound.