Actually on the basis of my limited knowledge on Muhajirs from observation at PDF, muhajirs are actually the most proud of their Urdu/sub-continental heritage and Pak Punjabis the most likely to claim some foreign lineage. I could be wrong though..
The time I was on PDF, years back, it was run by a bunch of Hindko chaps posing as full on Pashtuns, i.e., Neo and Jana. They decided to deride Indian members in their native tongue, forgetting the fact that Hindko is, to a large extent, intelligible to Punjabi speakers! When I called them out on their facade, and asked them to speak in Pashto, rather than Hindko, they flatly refused! Obviously, they didn't know Pashto and were putting up a facade!
The so called "Pak Punjabis" on that forum are a similar story. Several claim to be Pak Punjabis and put on a charade, but when pressed on why they don't know a word of Punjabi, they eventually claimed to be "half-Muhajirs". Some, who beat their chest at being foreign, are most likely from the backward Punjabi castes/clans.
That said, online forums are actually an extremely poor guage to judge a people, especially when you can't talk to them face to face. You have to get to know the people personally to get an insight into them. Pakistanis are great people, but they have an inherent inferiority complex, all thanks to the BS country which they ended up with. Infact, their hatred of India too is to shield their inferiority complex and to feel important.
I have many Pakistani Punjabi friends who openly talk about their grandfathers or great-grandfathers being Kashmiri Pandits, or well known Sikhs; and these guys even have their recorded family history passed down from generations, and are even able to tell you their forefathers exact Hindu or Sikh names! On the other hand, I know of a recent Pakistani Punjabi immigrant girl, straight from a village in Gujranwala district, who is fixated at trying to look "Arab" or "Egyptian", but plays totally dumb and claims to have never heard the words "Gujjar", "Jatt", "Rajput", etc, etc.
The thing is, Punjab actually does have many "foreign origin" clans, such as the Bastis, Sheranis, Lodhis, Turkhals, Niazis, and many more! However, they are well integrated Punjabi speaking people, and are actually no different than the other Punjabi clans in terms of hierarchy. Some of these foreign clans are considered peasants, some of them are Zamindars. Simply being foreign doesn't make them above rest of the clans; therefore, the actual Punjabis don't make such a big issue out of it, as much as the pseudo-foreigners do.