After reading the discussion you linked to, I think user, brilliantpink, has a very good answer:
The construction "to be seen to do something" is indeed correct, but
uncommon. It means exactly the same as "to be seen doing something".
The only difference, in my opinion, is that "to be seen to" puts the
emphasis on the seeing rather than the action being done. It might be
used in a legal case, or another situation where there is a question
of whether the person actually 'crossed the street' or not, or whether
they are guilty of some other act that followed. "Well, he was seen to
cross the street" (someone says they saw him, so we know he must have
crossed the street, but we don't know what he did after that).
Important: This construction is used only in the passive, and perhaps
that is why it strikes people as odd. Not "I saw him to cross the
street" but only "He was seen to..."
Another aspect that is touched on in that discussion is when reading "He was seen to cross the street", I infer a sense that "He" has a habit of crossing the street.
It resembles the turn of phrase, "He is known to...", which is used to describe a characteristic or habit of someone. For example:
- He is known to smoke two packs a day.
- He is known to be afraid of dogs.
- He was known to bring flowers to his mother weekly.
- The club was known to exclude people of color.
Technically, the two sentences could mean the same thing. However, I assume that if the speaker chooses to use the more unnatural phrasing, they mean to imply something extra.