This looks like a bug.
Actually, regardless of whether there was interception or not, this is bug: when you spy on someone, you certainly don't want to make that person aware of the spying. But in this case, I'd rather incline towards a more mundane buffering issue.
In phone networks, especially mobile networks, audio data is split into individual packets which are then sent to the receiver and meant to be reassembled into due order. Various technologies are employed for the data transit and some (most) of them use buffering at some point. For audio data, it makes little sense to keep a packet for a long time, because the receiver, at one point, decides that it has waited for long enough and plays whatever was received, even if there are holes. That's the common characteristic of media data: there are latency constraints, so lost or late packets must be accommodated through interpolation. Thus, buffered packets will commonly be marked with a time stamp which allows for an expiry process.
I can imagine that a buffering systems may get it wrong with the time stamping under rare conditions, e.g. if the machine's clock was unduly reset at the same time. This may induce the effect observed by your wife.
(More generally, programming blunders are way more common than genuine spying. Thinking otherwise requires assuming that people working for spy agencies are utterly more competent than the rest of the IT industry, which is not plausible,
James Bond notwithstanding.)