The reason is that try is a two-place predicate that assigns an Agent theta role to Mary and a Theme (or similar) role to its infinitival complement, whereas seems is monadic (in your example), must assign just one theta role, to its complement, and cannot have a second argument in its specifier to which it can assign Agent (or any other) role. [Of course, seems may also be two-place, e.g., in It seems to me that Mary is an excellent teacher, but in that case it must have two 'internal' arguments, and assign a Theme role to the subordinate clause and an Experiencer role to the PP complement to me; under no circumstances can it assign an Agent role to the PP to me, because Agent is never assigned to an internal argument in complement position; Agent can only be assigned in Spec v/V position, and, of course, never by a non-agentive verb like seems].
As a consequence of that difference in argument structure between try and seem, in a sentence like Mary tried [PRO to be there] a PRO is needed in the subordinate clause to discharge the Theme role projected by the predicate be there and some other argument (Mary, in this case) is also needed to discharge the Agent role assigned by try in the upper clause to its own Spec V. If you had only one argument, i.e., if you base-generated Mary as the specifier of be (there) in the subordinate clause, and then raised it into the Spec of the higher verb try, the chain formed by Mary in Spec try and its trace in Spec be (or by the two copies of Mary, under the 'Copy Theory of Movement') would receive two theta roles (Agent and Theme, respectively), the Theta Criterion would be violated, and the derivation would be ungrammatical. (Under later versions of Chomskian grammar, of course, that Theta Criterion violation need no longer be invoked to block the derivation: since Mary already has a valued role attribute in Spec be, it could never be raised into a higher thematic position, e.g., Spec try, because there would be no feature to check in Spec try and Economy would automatically forbid that movement. Mary could still raise, of course, but not in search of a second theta role; it could raise directly into Spec Tense, for example, to check its Nominative Case feature there, but it would have to do so skipping Spec try, and therefore would never get assigned a second theta role as Agent of try anyway.
On the contrary, in a sentence like Mary seems [t to be there] (where, recall, seems is monadic and assigns a theta role only to its complement, not to its specifier), replacing 't' with a PRO in the subordinate clause would make the sentence ungrammatical, because, in that case, it would be PRO that would receive the only undischarged theta role available in the sentence (the Theme role assigned by be there). Mary, on the contrary, would not receive any theta role in Spec seems, and, again, the Theta Criterion would be violated (by defect, in this case) and the sentence would be ungrammatical. If Mary is base-generated as a Spec of be there, though, it gets the Theme role assigned by be there, and, as the higher verb seems does not assign any theta role to its own specifier, Mary never receives a second theta role, the Theta Criterion is not violated, and the sentence is well formed.