"Arranged marriage" in an Indian context doesn't necessarily imply "parents tell you who to marry".
In many cases it's essentially parent-involved matchmaking. There may be a professional matchmaker or family astrologer who sources leads. The prospective bride and bridegroom consider multiple or even dozens of options, and discuss their favorites with their parents or other close relatives. The bride/groom visit each other a few times, with families in tow. After they reach an agreement, there's a few months-long engagement. The couple may stay in touch by telephone, social media, video calls, (often chaperoned) in-person visits, and so on. If either person finds a major red-flag during this time, they have the (rarely-used) nuclear option of breaking the engagement.
(Source: I know Indian couples who have "arranged marriages" in the way I described).
> She said compatibility was the most important thing, not love, which I found very interesting.
Isn't that considered important in the West too? Advice such as "you have to agree on money, children, and religion; everything else is negotiable" or "you have to be able to make each other laugh" is thrown out pretty frequently. It's generally understood that relationships have a honeymoon phase, after which compatibility is a major factor in staying together. People who get married young sometimes don't understand this fully.