It might have been custom built with very light barrels, and already overbored, or any number of other things, but I doubt it. How old is it? I don't remember the older 16 gauge pressure limits, or if they were any different than the modern ones, but I think they were/are the same. All current American manufactured shotgun shells are limited to the SAAMI specifications, and with modern progressive powders velocities are obtained even easier with lower pressures than the max. If it was designed for smokeless powder you are likely okay, but I would do my homework and do some checking first. Parkers were never built light like English game guns to start with. I am not a huge fan, but they are/were good guns. As far as fluid steel barrels designed for smokeless powders, the number of them being shot with lengthened chambers probably outnumbers the ones that haven't been.
