Well, there may be a statute in Chicago that makes this the law but at common law this is not true.
A party to a contract has discretion to act or not act on a condition or breach of a condition by the other party. They can do this once or a dozen times without necessarily waiving their future entitlements. An exception is where they choose not to act all of the time; in such a case unless there is evidence to the contract a court will usually find that the condition has been permanently waived.
Notwithstanding, exercising such discretion would have no impact on other contracts unless the exercise of discretion was done in an unlawfully discriminatory way (e.g. always waiving the fee for African Americans but never for other races).
Under common law, this would be a liquidated damages clause i.e. a payment for their costs in dealing with your breach. Such clauses must be a genuine pre-estimate of the actual costs incurred; if they are not then this is a penalty clause and unlawful - you may want to ask then to justify how the fee is a reflection of their costs in your being 1 day late.
I can't speak for Illinois but in Australia, the making of the statement would be misleading and deceptive conduct, a strict liability offence (i.e. it doesn't matter if they were trying to mislead or not) with significant ($1 million+) fines.