Depends on their income and other commitments. If someone has a budget, it's presumably for a reason. If eating out is the #1 cause of breaking a budget, then it certainly can be the piece that sends them into other budget problems.
Median income in, for example, Detroit was $58,411 in 2017. Post-taxes that would be $45,484. $3300 is about 7.3% of that so, yeah, that's a pretty hefty bite.
Even assuming the median earner is paying the average for eating out (e.g. is a blue collar family of 4 in the Midwest spending the same proportional to income eating out as a childless professional couple on the coast? I'd wadger no.), you still need to compare that against the cost of groceries. So, it's more of an additional 3%-5% in reality, not a whole 7%.
This is only around 20-25% of the median discretionary income in the US i.e. money available for savings after all ordinary expenses. So while it can have a significant impact on savings rate, I would agree that it is misleading to state that this will make you "broke".
Being broke requires spending the other 75-80% of discretionary income too, and that is a much larger pool of money.