Should I be using assert in my PHP code?

The rule of thumb which is applicable across most languages (all that I vaguely know) is that an assert is used to assert that a condition is always true whereas an if is appropriate if it is conceivable that it will sometimes fail.

In this case, I would say that assert is appropriate (based on my weak understanding of the situation) because records should always be set before the given method is called. So a failure to set the record would be a bug in the program rather than a runtime condition. Here, the assert is helping to ensure (with adequate testing) that there is no possible program execution path that could cause the code that is being guarded with the assert to be called without records having been set.

The advantage of using assert as opposed to if is that assert can generally be turned off in production code thus reducing overhead. The sort of situations that are best handled with if could conceivably occur during runtime in production system and so nothing is lost by not being able to turn them off.

Think of asserts as "power comments". Rather than a comment like:

// Note to developers: the parameter "a" should always be a number!!!

use:

assert('is_numeric(a) /* The parameter "a" should always be a number. */');

The meanings are exactly the same and are intended for the exact same audience, but the first comment is easily forgotten or ignored (no matter how many exclamation marks), while the "power comment" is not only available for humans to read and understand, it is also constantly machine-tested during development, and won't be ignored if you set up good assert handling in code and in work habits.

Seen this way, asserts are a completely different concept than if(error)... and exceptions, and they can co-exist.

Yes, you should be commenting your code, and yes, you should be using "power comments" (asserts) whenever possible.