"All spells must come from the same class's spell list." I have a player running a Summoner who wants to use spells off the paladin spell list. At 4th tier he can take spells that clerics or oracles would need to be 15th level to cast. I have grave misgivings over how overpowered this could become but can't find anything published prohibiting it.
Your assumption is correct, there is no reason a player couldn't select paladin and get some nice 4th level spells.
There are only a few spells that paladin's get lower then other classes and they are mostly buffs with short durations. Archon's trumpet would be an exception, but the dc would be low.
A tier 4 mythic character should be at least level 8, if not closer to 10, at which point a powerful buff once a day shouldn't be a huge issue (or even a trumpet with a low dc). If the player took mythic archon they would be able to get the spells at tier 2--more around 4th-6th level, which could be harder to deal with.
It shouldn't be that hard to manage really. If you think it is perhaps talk with the player and ask that they don't do this until later and toss them some bonus XP or whatever. You could always pull out the GM trump card if you can't manage it and disallow it, but there are usually better ways to handle things.