Your admin got it real wrong (or there was some translation mishap).
TLS 1.1 and 1.2 fix some issues in TLS 1.0 (namely, predictability of IV for CBC encryption of records). It is possible to work around this issue in TLS 1.0, but it depends on how hard the implementations work at it. So, in that sense, TLS 1.1 and 1.2 are more secure than TLS 1.0, since they are easier to implement securely.
The so-called "heartbleed" is not a protocol flaw; it is an implementation bug that is present in some OpenSSL versions (OpenSSL is a widespread implementation of SSL/TLS, but certainly not the only one). When an OpenSSL version has that bug, it has it for all protocol versions, including TLS 1.0. Thus, when heartbleed applies, it equally applies to TLS 1.0, TLS 1.1 and TLS 1.2. When it does not apply, well, it does not apply.
The source of the confusion is that your admin (or his sources) does not appear to understand or conceptualize the difference between protocols and implementations. TLS 1.0 and TLS 1.2 are protocols described in relevant standards (RFC 2246 and RFC 5246, respectively). A protocol says what bytes must be sent when. An implementation is a piece of software that runs the protocol. OpenSSL is an implementation. It so happens that the "heartbleed" bug occurs in the implementation of a relatively new protocol feature (the "heartbeat extension") that very old OpenSSL implementations don't know about. Thus, very old implementations of OpenSSL don't suffer from heartbleed (though they have other serious issues, being very old). The same very old implementations don't know about TLS 1.1 and TLS 1.2 at all. Thus, in the mind of your admin, the two independent facts coalesced into a single (but flawed) mantra, that wrongly says that heartbleed is a security issue of TLS 1.1 and 1.2.