This is not actually a quote-within-a-quote. The only quoted words here are "every effort".
… Bank declined to interview, but in a phone call said, "We are making...
is actually all part of the newscaster's statement. The words quote and unquote are used here to denote that the two words contained therein are a direct quote, i.e. the specific words used by the bank spokesperson, in that order. The rest of the statement "We are making..." is essentially paraphrased to give the gist of what has been conveyed. This is extremely common in televisual, audio and written journalism to distinguish between the two ways of conveying information given by a second party (directly quoting versus interpreting or paraphrasing what may be technical or wordy information).
Any change in the newscaster's tone will indicate their personal (or the station's) opinion on the quoted words, and can not have any effect on the original speaker's message, only on how it may be received by the listener watching the show. In other words, it is not misquoting, simply introducing editorial opinion. How one feels about this behaviour influences which news sources they choose to consume, although it is becoming more and more difficult to find unbiased sources these days.