I have been told that foreign travelers are banned from having their bags plastic wrapped when going through security at a US airport?
Is this true?
Unknown, but: Long ago I locked a suitcase full of electronic gear when travelling SF-London. The customs men came out and asked for the key. Thoughtful of them - a broken lock would have been within the rules. Alas, the case also held a large container of dairy whitener placed in it during packing. It has a clip shut spout for normal use AND the whole top was pressed on after filling. For whatever reason it appears the customs people opened the container by removing the sealed for life press on join, and did not reseal it properly. The white powder got ALL through EVERYTHING in the bad. It was beautifully deliquescent. All sorts of gear was gummed up with sticky moist powder. (I had fun dismantling a DVD writer in a Belgian motor camp and washing all the pieces in the washroom basin. A 12vdc/230VAC converter failed in Holland. May or may not have been due to powder clogging of heatsink. )
Relevance: Making life easy for the security people is "a good idea". Wrapping gear seems likely to attract their attention. If not necessary then a "cinch tight", clip together strap (available here for a few dollars) or several may be a better idea.
And, put the dairy whitener in another bag.
Until about 5 years ago it was possible to have this plastic wrapping service done at LAX. Now you can't have the service done! LAX and SFO were the only American airports that I ever saw plastic wrap being done in. I have tried buying a big roll of the plastic wrap that moving companies sell to wrap their furniture in. It is very difficult to wrap your own heavy bags! They were accepted for flight at LAX even though they were wrapped.
There are no rules against wrapping your bags with plastic film.
If TSA decides they want to inspect your bag, they will cut the film off and will not re-wrap it. So it is up to you to decide to pay to have it wrapped and hope TSA doesn't cut it off wasting your money.
If you are flying in from an international destination and connecting/rechecking to a domestic flight, TSA opens a far greater percentage of those bags for secondary inspection. So this rumor could have come from a great number of bags arriving at domestic locations sans wrap.