It´s just that some natives do not find it enough or even do not recognise the passive meaning and add another passive suffix.

Grammatically correct way:

de-n-mek is the passive of de-mek

söyle-n-mek is the passive of söyle-mek

etc.

I usually do not read translation forum. So they naturally go unnoticed by me.

Illogical forms appear in every language. The question is when they are accepted into standard language. At some point usually language planners give up. What was the name of the Turkish language authorities´ board again? Do they have a web site? (Just for interest...)

I have an explanation for this situation. Most of the time we make a verb passive adding (i)l suffix. Ex: git - il - di. So I think some people subconsciously think only (i)l suffix make verbs passive and they think "n" as a buffer letter. So they add (i)l after n. So Abla you see even the irregularities in Turkish have a logic. 

It seems you are right, gokuyum. A very quick search brought up double passives for verbs like

         uyunmak (>*uyunulmak)

         beklenmek (>*beklenilmek)

         beslenmek   (>*beslenilmek).

Obviously it has something to do with the passive marking –n which speakers feel is “not enough” or something.

But not all double passive forms ended up in the dictionary like denilmek did. This is only a guess from me but maybe the connection with demek is easier to forget because of the irregularities in its stem vowels and that’s why the more regular (and yet one syllable) den- is considered the imaginary basis of the passive form.

The passive form of a Turkish verb is formed by adding (-ı,-i,-u,-ü l/n to its root or stem:

1) We add -ıl,-il,-ul,-ül to the verbs end in a consonant:

otur.ul, san.ıl, bak.ıl, çoğalt.ıl, iç.il, göm.ül, ban.ıl, kap.ıl, ser.il, as.ıl, it.il, ay,ıl, kaz.ıl, sev,il, sağ,ıl

l is exception (-ın,-in,-un,-ün):

kıl.ın, bil.in, gül.ün, bul.un

2) We add -n to the verbs end in a vowel: 

söyle.n, ara.n, oku.n, de.n, yıka.n

We also use the same suffixes to make reflexive form of some exact verbs.

For example yıkan can be both passive and reflexive.. please, study the examples below:

Ali yıkandı ve giyindi (both verbs are reflexive)

Ölü yıkandı ve gömüldü(both verbs are passive) 

The verbs that are originally reflexive  (kop, bat, etc) have no passive form.

But you can see people adding (passive)-il to a word which is already suffixed by (reflexive)-(i)n or -(i)n which is not clear enough if it is passive:

yıka.n.ıl, giy.in.il, söyle.n.il, de.n.il etc.

So the combination is: reflexive+passive (not passive+passive)

The question is: is this combination grammatically correct?

I am not sure if it is totally incorrect..

Which one sounds better to the native speakers?

a) böyle de giyinmez ki

b) böyle de giyinilmez ki

?

note: any addition, contribution or objection is welcomed.

Interesting. Two ways to see it. Which means it was maybe not a totally stupid idea to suspect a reflexive marking in the verb in the first place.

Reflexive: Agent=Patient. How can you make a passive out of it?

This is a tough one. I am not sure I know. But it has to do with the impersonal usage of Turkish passive which is a special feature of it. Of course I would miss it completely is there wasn´t a similar thing in Finnish. That´s why I understand completely when scalpel says

         yıka|n|ıl|dı = ´wash´ + ´himself´ + ´is done´ + ´sometimes in the past´.

(Well, this is not what he said but this is how I understood it.)

In Finnish it would be

         pese|ydy|t|ti|in = ´wash´ + ´self´ + ´is done´ + ´sometimes in the past´ + poss sg 3rd,

which means some people (probably more than one) washed themselves in the past. This is our passive. It can be formed from intransive verbs as well as transitive. It is used for reflexives as well. When we use impersonal passive we always mean that some people did the action, we just don´t know who.

Geoffrey Lewis writes: "The most remarkable feature of the Turkish passive is its impersonal use: niçin yalan söyle-n-ir? ´why are lies told?, i.e. ´why do people tell lies?´ In this example the passive verb appears to have a subject, but impersonal passives are also regularly formed from intransitive verbs and then have no conceivable grammatical subject..."

I also like the Wikipedia article about impersonal passive. There are some Turkish and German examples there.