whats going on here?

I gotta crash, so I aint got time to read the TAB, but.....

if it's in the key of D major, then an A major chord is the 5th chord you can build off the D major scale, so it would fit perfectly. Likewise, A is the 5th note in the D major scale, so I'm not sure what the problem is.

D major scale - D E F# G A B C#

Chords from that scale - D major (D, F#, A), E minor (E, G, B), F# minor (F#, A, C#), G major (G, B, D), A major (A, C#, E), B minor (B, D, F#), C# dimished (C#, E, G).

oops, I meant a C chord.

I also found this little trickster:

http://www.chordie.com/chord.pere/getsome.org/guitar/olga/chordpro/p/Tom.Petty/TooGoodToBeTrue.chopro

5 different major chords, I'm sure there's some weird explanation, but I've looked at using the circle of fifths/fourths and key changes between verses and choruses and see no explanation, yet it all fits very well and accurate to the original song.

The bVII chord (C in this case) and it's root, the b7 note, is so common in rock/pop/folk/blues that it hardly even qualifies as an exception.

You can think of it as being borrowed from the Mixolydian or the parallel minor if you like or you can think of it as a brief key change into the 5 key. However you wrap your head around it, it is crucial in all rock and derived music.

As for your second example, the Tom Petty song, it's important to realise that pop musicians like major chords. Tom's song is technically in E minor with a chorus in D, but he prefers a major sound so he uses E major and A major instead of Em and Am (B, the V, is almost always major anyway). You could also think of it as E major borrowing the bIII (G) from the parallel minor and modulating into D major in the chorus.

To sum up, it's common to freely mix chord from a major key and its parallel minor.