Channel Form is not inserting <p> tags like Channel Entries does; all <p> tags mysteriously gone from entries

Question

When we enter properly formatted HTML into the RTE via the CP, the <p> tags are present. But when we use the {exp:channel:form ...} we lose all the <p> tags but retain all other tags. We're using Textarea (Rich Text) fields because we need the RTE on our custom dashboard.

I tested the {exp:channel:entries ...} and the <p> tags were properly retained.

So what could be causing this? How can we fix it? We need the channel form to output the proper tags because we have a live preview of what's in the populated textarea elements.

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Update:

When using {field:my_channel_field} the <p> tags are retained, but the RTE isn't created. It's just a textarea with html/text.

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Update 2:

I did some digging and found that in the SQL tables there are no <p> tags, meaning that they're inserted when the data is called.

For instance this is what's actually in the Database

<h3>Lorem nascetur </h3> Porttitor. Integer nunc. Hac ultricies velit magnis. Nunc est, tortor proin? 

And this what is output when using {exp:channel:entries ...}:

<h3>Lorem nascetur </h3>

<p> Porttitor. Integer nunc. Hac ultricies velit magnis. Nunc est, tortor proin?</p>

So at some point the <p> tags are being injected into the document, and I want to know how can I force this so they are in the RTE when the user goes to edit them within an {exp:channel:form ...} loop?

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Update 3:

I found these in /system/expressionengine/modules/rte/libraries/Rte_lib.php on lines 445 to 446

// Strip paragraph tags
$data = preg_replace("#<(/)?pre[^>]*?>#i", "<$1pre>", $data);
$data = preg_replace("#<p>|<p(?!re)[^>]*?".">|</p>#i", "",  preg_replace("#<\/p><p(?!re)[^>]*?".">#i", "\n", $data));

and

if (stristr($str, '<p') !== FALSE)
{
    $str = preg_replace("#<(/)?pre[^>]*?>#i", "<$1pre>", $str);
    $str = preg_replace("#<p>|<p(?!re)[^>]*?".">|</p>#i", "",  preg_replace("#<\/p><p(?!re)[^>]*?".">#i", "\n", $str));
}

in /system/expressionengine/libraries/EE_Typography.php.

Commenting them out didn't seem to solve the problem

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Update 4:

I tested my theory more completely by simply doing a {exp:channel:entries ...} and {exp:channel:form ..} on a blank template with nothing other than a field.

When output, the channel:form actually outputs HTML tags (<h3> from update 2 above) that never get rendered, and the channel:entries outputs the correct HTML and does get rendered. See picture:

Answer 1

After much consternation I tried commenting out the Strip paragraph tags section of the save_field() function from above again, but tested it more thoroughly and it works. It keeps the tags on submission/repopulation through channel:form. This might cause bugs down the line, but it'll do for now.

/system/expressionengine/modules/rte/libraries/Rte_lib.php

lines 445 to 447.

// Strip paragraph tags
/*
$data = preg_replace("#<(/)?pre[^>]*?>#i", "<$1pre>", $data);
$data = preg_replace("#<p>|<p(?!re)[^>]*?".">|</p>#i", "",  preg_replace("#<\/p><p(?!re)[^>]*?".">#i", "\n", $data));
*/