I have the impression that much of this "'tunnel' hearing" is a result of Polish people not expecting foreigners to speak their language.
That's very possible. But for those Poles that have never studied English, the pronunciation of Polish by English visitors may sound shocking for several reasons:
1. English is essentially a language that uses vowels no other language would accept. :-)
This is a joke of course, but with a lot of truth in it. Polish has only several vowels, all of the same length, all open. English is much reacher in this department, but yet English speakers have trouble with apparently simple Polish open vowels. Take for example a simple given name "Jan". While it is comparatively easy to explain to English speakers that several countries in Continental Europe pronounce "J" like "Y" (as in Yann), not like "G" (as in Gina) it is harder to explain the pronunciation of the open vowel "A". Most what you can get from a typical English speaker is English Ian or Yawn. Chinese are even worse here: most of them pronounce it like a long "Yea".
2. English speakers have their own understanding of pronunciation of Romance languages, including Latin. English instructions on proper pronunciation of Italian, for example, are particularly baffling. Why do they have to make such simple stuff so complicated? :-)
In contrary, Poles have no problem with Italian or Spanish vowels at all.
This could be nicely demonstrated by comparing pronunciation of "Julius Caesar" using four Latin pronunciation methods. With English this gives particularly comical results because English pronunciation had undergone drastic changes at the end of the Middle Ages:
YOO-lee-us KYE-sahr (reconstructed ancient Roman)
YOO-lee-us (T)SAY-sahr (northern Continental Europe)
YOO-lee-us CHAY-sahr (“Church Latin” in Italy)
JOO-lee-us SEE-zer (“English method”)
So when a native Pole hears something that sounds to him as "Dżulius Size", he gets no connection with "Juliusz Cezar".
3. And there is of course the Polish labyrinth of digraphs and trigraphs. For an English speaker, who never studied Polish, the consonants are particularly puzzling. Here is how Uncle Google and Ivona.com pronounce some Polish words, and this probably what a Polish local hears when spoken by an English tourist:
Pszczyna ==> P'skizyna, Szczyna
Tyskie ==> Tajski (Thai ski), Tyski
Żywiec ==> Ziłik or Zyłjak
Jak się masz? ==> Dżak si mas?
Jak masz na imię? ==> Dżak mas zna imi?