The mutual fund is legally its own company that you're investing in, with its own expenses. Mutual fund expense ratios are a calculated value, not a promise that you'll pay a certain percentage on a particular day. That is to say, at the end of their fiscal year, a fund will total up how much it spent on administration and divide it by the total assets under management to calculate what the expense ratio is for that year, and publish it in the annual report. But you can't just "pay the fee" for any given year.
In a "regular" account, you certainly could look at what expenses were paid for each fund by multiplying the expense ratio by your investment, and use it in some way to figure out how much additional you want to contribute to "make it whole" again. But it makes about as much sense as trying to pay the commission for buying a single stock out of one checking account while paying for the share price out of another. It may help you in some sort of mental accounting of expenses, but since it's all your money, and the expenses are all part of what you're paying to be able to invest, it's not really doing much good since money is fungible.
In a retirement account with contribution limits, it still doesn't really make sense, since any contribution from outside funds to try to pay for expense ratios would be counted as contributions like any other. Again, I guess it could somehow help you account for how much money you wanted to contribute in a year, but I'm not really sure it would help you much.
Some funds or brokerages do have non-expense-ratio-based fees, and in some cases you can pay for those from outside the account. And there are a couple cases where for a retirement account this lets you keep your contributions invested while paying for fees from outside funds. This may be the kind of thing that your coworker was referring to, though it's hard to tell exactly from your description. Usually it's best just to have investments with as low fees as possible regardless, since they're one of the biggest drags on returns, and I'd be very wary of any brokerage-based fees when there are very cheap and free mutual fund brokerages out there.