True or a wind-up
Actually most English speakers pronounce something between sz and si.
The second two can and often are distinguished but many Poles don't pronounce them differently in rapid casual speech.
Do you live in Cracow maybe? ;)
Ah, so the Google audio of the Polish word for please is some sort of textbook speak from the past?
I would say more like actor's speech. However she pronounce it too clearly, no Pole would put so much efford in one word as she does ;)
Nasals "ę" an "ą" are typically slurred over royally in everyday speech. Even I tend to blur their distinction, unless of course I'm over-pronouncing them for a non-Pole to hear this (albeit academic) distinction.
And that's how it should be pronounced - a bit slurred way (I mean ę at the end of word)
Does she miss the p sound at the start of przepraszam?
No, she clearly says p. However I must pick on the way she accents this words, she should not pronounce the accented syllable so long.
don't you agree then that the majority of Poles also seem to be saying piglet?!
Definitely no. Between si and sz the difference is clear for a Polish ear.
The same way as Pole can have a problem to distinguish between some English sounds, you as an English speaker can have problem with distinguish some Polish sounds. You are not the first one to have problems with si and sz (in English you have sh which is a sound between si and sz), or p before rz (which is pronounced as sz after p). Both difficulties are common among English speakers.