They typically contain copper, silver, lead, and tin, but those don't leach out of them at a significant rate, and of those four heavy metals, only lead is a real toxicity risk even if you digest the panels in acid instead of leaving them out in the rain. Another comment suggests that the dopants in the silicon are the relevant heavy metals, but those are present at parts-per-million levels, locked inside the silicon's diamond-structures crystalline lattice, and passivated with silicon dioxide, so that's not plausible either.
The most likely explanation is that this is a lie.
CdTe solar panels [0] do, but it's a bit of red herring because almost nobody is using those panels for large scale installations (they're mainly used where being "thin and light" is important. The common crystalline silicon panels [1] don't have any major toxic components.
Solar panels are giant photodiodes. Heavy metal doped silicon. a-Si something or SiGe or GaAs or InP or whatever pairs and trios of toxic metals. Generally more toxic more electronically open to trade therefore broader spectral response and better performance. You can't do, say, Al substrate PtFeCu semiconductor, that's not going to make sense.
They're not merely similar to a photodiode, but using giant photodiodes as batteries is literally the idea.
There are some versions based on toxic organic chemicals in place of toxic inorganic elements, few and far between, and I guess the technology will eventually move onto engineered nanoparticles later in this century after they've cracked fusion, but that hasn't happened yet.
The most likely explanation is that this is a lie.