Here and on most cryptocurrencies it seems like historically the orange BTC price line is always below the green USD line.
in a chart like this, being "below" or "above" is a matter of scale that the chart uses. i can simply change the Y axis and get a different "below and above" lines.
the only thing you can compare on a chart like this is the way the change occurs. meaning price against USD goes up as price against BTC goes up and vice versa.
this is what i mean, a chart with same values but different Y scaling:
When this is the case, I assume that fluctuations in BTC price drive the price of the altcurrency.
it does but you can not make the conclusion based on previous statement.
No different than me saying my Google stock is now more valuable because the value of the dollar has risen. I have no idea if this assumption is correct. Where I get really confused is when I see the lines intersect and USD goes above BTC. Does this mean the currency is growing at a faster rate than BTC if it intersects?
you can say that, but what is really happening is that the ETH/BTC market is more active so when bitcoin price is rising in order for ETH to keep its price the same it has to drop against BTC but people usually don't care about USD value of an altcoin, they do care about its BTC value so if it goes down against bitcoin they start buying it hence creating some sort of resistance. and if it drops slower against BTC it means its USD value is rising too.