Biochemist here! The DNA polymerase reaction can only take place when the gene is unwound from the histone in the first place. Therefore the PCR wiki page will not provide you with the answer... The key is the "DNA purification" prep step where you digest the histones with proteases.
This is not really right. The high duplex denaturing temperature of the initial thermocycle will usually also denature histones and unwind them from the dna. That's why thermocycle procedures for raw samples have a long initial denaturation (5-10 min) and thermocycle procedures for prepurified DNA need not have such a long initial incubation at 95 C.
Did you guys all skip the DNA extraction practical at university?
1) Proteinases are indeed not necessary.
2) The step that removes any DNA bound proteins and in fact denatures the vast majority of proteins is the salting out. DNA is negatively charged. Proteins bind DNA by being positively charged. When you add a lot of salt, you add a lot of ions that compete for those ionic bonds. Proteins fall of the DNA, and will eventually be denatured.
3) The long initial incubation in some PCR protocols is mostly a relic from old times when there weren't any commercial extraction kits and contamination with residual RNA was a potential issue. A modern setup doesn't need it (but many keep the step anyway because why would you remove it when it doesn't hurt to do it anyway).
Different programmes will place more or less emphasis on different things. For myself, this was a tiny part of a 4-year undergraduate degree and I probably didn't spend any more than a day or two on the topic.
What you say does sound right, but I think the other answers still have pedagogical value. Thanks for clearing this up, I now realize I need to brush up on this topic.
See here: https://en.wikipedia.org/wiki/DNA_extraction